共查询到20条相似文献,搜索用时 125 毫秒
1.
In Finsler geometry, minimal surfaces with respect to the Busemann-Hausdorff measure and the Holmes-Thompson measure are called
BH-minimal and HT-minimal surfaces, respectively. In this paper, we give the explicit expressions of BH-minimal and HT-minimal
rotational hypersurfaces generated by plane curves rotating around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski (α, β)-space
(\mathbbVn+1,[(Fb)\tilde]){(\mathbb{V}^{n+1},\tilde{F_b})} , where
\mathbbVn+1{\mathbb{V}^{n+1}} is an (n+1)-dimensional real vector space, [(Fb)\tilde]=[(a)\tilde]f([(b)\tilde]/[(a)\tilde]), [(a)\tilde]{\tilde{F_b}=\tilde{\alpha}\phi(\tilde{\beta}/\tilde{\alpha}), \tilde{\alpha}} is the Euclidean metric, [(b)\tilde]{\tilde{\beta}} is a one form of constant length
b:=||[(b)\tilde]||[(a)\tilde], [(b)\tilde]\sharp{b:=\|\tilde{\beta}\|_{\tilde{\alpha}}, \tilde{\beta}^{\sharp}} is the dual vector of [(b)\tilde]{\tilde{\beta}} with respect to [(a)\tilde]{\tilde{\alpha}} . As an application, we first give the explicit expressions of the forward complete BH-minimal rotational surfaces generated
around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski Randers 3-space
(\mathbbV3,[(a)\tilde]+[(b)\tilde]){(\mathbb{V}^{3},\tilde{\alpha}+\tilde{\beta})} . 相似文献
2.
A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold ${\widetilde M}A locally conformally K?hler (LCK) manifold M is one which is covered by a K?hler manifold [(M)\tilde]{\widetilde M} with the deck transformation group acting conformally on [(M)\tilde]{\widetilde M}. If M admits a holomorphic flow, acting on [(M)\tilde]{\widetilde M} conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable
under small deformations. We define a new class of LCK-manifolds, called LCK manifolds with potential, which is closed under
small deformations. All Vaisman manifolds are LCK with potential. We show that an LCK-manifold with potential admits a covering
which can be compactified to a Stein variety by adding one point. This is used to show that any LCK manifold M with potential, dim M ≥ 3, can be embedded into a Hopf manifold, thus improving similar results for Vaisman manifolds Ornea and Verbitsky (Math
Ann 332:121–143, 2005). 相似文献
3.
L. Sanguiao Sande 《Geometriae Dedicata》2011,151(1):305-321
4.
Pierre Angl��s 《Advances in Applied Clifford Algebras》2011,21(2):233-246
This self-contained short note deals with the study of the properties of some real projective compact quadrics associated
with a a standard pseudo-hermitian space H
p,q
, namely [(Q(p, q))\tilde], [(Q2p+1,1)\tilde], [(Q1,2q+1)\tilde], [(Hp,q)\tilde]. [(Q(p, q))\tilde]{\widetilde{Q(p, q)}, \widetilde{Q_{2p+1,1}}, \widetilde{Q_{1,2q+1}}, \widetilde{H_{p,q}}. \, \widetilde{Q(p, q)}} is the (2n – 2) real projective quadric diffeomorphic to (S
2p–1 × S
2q–1)/Z
2. inside the real projective space P(E
1), where E
1 is the real 2n-dimensional space subordinate to H
p,q
. The properties of [(Q(p, q))\tilde]{\widetilde{Q(p, q)}} are investigated. [(Hp,q)\tilde]{\widetilde{H_p,q}} is the real (2n – 3)-dimensional compact manifold-(projective quadric)- associated with H
p,q
, inside the complex projective space P(H
p,q
), diffeomorphic to (S
2p–1 × S
2q–1)/S
1. The properties of [(Hp,q)\tilde]{\widetilde{H_{p,q}}} are studied. [(Q2p+1,1)\tilde]{\widetilde{Q_{2p+1,1}}} is a 2p-dimensional standard real projective quadric, and [(Q1,2q+1)\tilde]{\widetilde{Q_{1,2q+1}}} is another standard 2q-dimensional projective quadric. [(Q2p+1,1)\tilde] è[(Q1,2q+1)\tilde]{\widetilde{Q_{2p+1,1}} \cup \widetilde{Q_{1,2q+1}}}, union of two compact quadrics plays a part in the understanding of the "special pseudo-unitary conformal compactification"
of H
p,q
. It is shown how a distribution y → D
y
, where y ? H\{0},H{y \in H\backslash\{0\},H} being the isotropic cone of H
p,q
allows to [(Hp+1,q+1)\tilde]{\widetilde{H_{p+1,q+1}}} to be considered as a "special pseudo-unitary conformal compactified" of H
p,q
× R. The following results precise the presentation given in [1,c]. 相似文献
5.
Leon A. Luxemburg 《Journal of Fixed Point Theory and Applications》2011,9(2):197-212
For a dynamical system X on a compact differentiable manifold M and for the dynamical system X(ρ) induced from X by a covering map r : [(M)\tilde] ? M{\rho \, : \, \widetilde{M}\, \rightarrow \, M}, we develop algebraic topology methods for estimating the lower bounds on the number of codimension-1 surfaces (i.e., on
the number of index-1 equilibria of flows and their stable manifolds) on the boundary of regions of stability on [(M)\tilde]{\widetilde{M}}. We also develop methods for estimating the number of equilibria on the boundaries of stability regions of noncompact manifolds
with very general assumptions. Our methods allow us to obtain results for noncompact manifolds in cases when Morse–Smale approach
does not work. 相似文献
6.
Semra Öztürk Kaptanoğlu 《Complex Analysis and Operator Theory》2010,4(4):901-904
Let X, [(X)\tilde]{\widetilde X} be commuting nilpotent matrices over k with nilpotency p
t
, where k is an algebraically closed field of positive characteristic p. We show that if X- [(X)\tilde]{X- \widetilde X} is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if [(X)\tilde]{\widetilde X} is of maximal rank. 相似文献
7.
Arvid Perego 《Mathematische Annalen》2010,346(2):367-391
The aim of this work is to show that the moduli space M
10 introduced by O’Grady is a 2-factorial variety. Namely, M
10 is the moduli space of semistable sheaves with Mukai vector v: = (2, 0, −2) in
Hev(X,\mathbbZ){H^{ev}(X,\mathbb{Z})} on a projective K3 surface X. As a corollary to our construction, we show that the Donaldson morphism gives a Hodge isometry between v^{v^{\perp}} (sublattice of the Mukai lattice of X) and its image in
H2 ([(M)\tilde]10, \mathbbZ){H^{2} (\widetilde{M}_{10}, \mathbb{Z})}, lattice with respect to the Beauville form of the 10-dimensional irreducible symplectic manifold [(M)\tilde]10{\widetilde{M}_{10}}, obtained as symplectic resolution of M
10. Similar results are shown for the moduli space M
6 introduced by O’Grady to produce its 6-dimensional example of irreducible symplectic variety. 相似文献
8.
For an embedded singly periodic minimal surface [(M)\tilde]{\tilde{M}} with genus r 3 4{\varrho\ge4} and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman–Wohlgemuth examples. We give
a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces. 相似文献
9.
Manuel del Pino Michal Kowalczyk Juncheng Wei Jun Yang 《Geometric And Functional Analysis》2010,20(4):918-957
Let (M,[(g)\tilde]){(\mathcal {M},\tilde{g})} be an N-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen–Cahn equation
e2 D[(g)\tilde] u + (1 - u2 )u = 0 in M,\varepsilon ^2 \Delta _{\tilde g} u \, + \, (1 - u^2 )u\, =\, 0 \quad {\rm{in}} \, \mathcal {M}, 相似文献
10.
A shadow price is a process [(S)\tilde]{\widetilde{S}} lying within the bid/ask prices S,[`(S)]{\underline{S},\overline{S}} of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless
market with price process [(S)\tilde]{\widetilde{S}} leads to the same maximal utility as in the original market with transaction costs. For finite probability spaces, this note
provides an elementary proof for the existence of such a shadow price. 相似文献
11.
Dani Szpruch 《The Ramanujan Journal》2011,26(1):45-53
Let
\mathbbF\mathbb{F} be a p-adic field, let χ be a character of
\mathbbF*\mathbb{F}^{*}, let ψ be a character of
\mathbbF\mathbb{F} and let gy-1\gamma_{\psi}^{-1} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic
function [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi ,s,\psi) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against y·gy-1\psi\cdot\gamma_{\psi}^{-1}. It turns out that γ and [(g)\tilde]\widetilde{\gamma} have similar integral representations. Furthermore, [(g)\tilde]\widetilde{\gamma} has a relation to Shahidi‘s metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi‘s local coefficient. Up to an exponential factor, [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi,s,\psi) is equal to the ratio
\fracg(c2,2s,y)g(c,s+\frac12,y)\frac{\gamma(\chi^{2},2s,\psi)}{\gamma(\chi,s+\frac{1}{2},\psi)}. 相似文献
12.
D. A. Trotsenko 《Complex Analysis and Operator Theory》2011,5(3):967-984
We continue to study upper sets ${\widetilde{A}=\{(x,r)\in A\times R_+ :\exists y\in A\setminus\{x\}, r=|x-y|\}}
13.
This paper has two parts. In the first part, we study shift coordinates on a sphere S equipped with three distinguished points and a triangulation whose vertices are the distinguished points. These coordinates
parametrize a space
(S)\widetilde{{\cal T}}(S)
that we call an unfolded Teichmüller space. This space contains Teichmüller spaces of the sphere with
\frak b{\frak b}
boundary components and
\frak p{\frak p}
cusps (which we call generalized pairs of pants), for all possible values of
\frak b{\frak b}
and
\frak p{\frak p}
satisfying
\frak b+\frak p=3{\frak b}+{\frak p}=3
. The parametrization of
[(T)\tilde](S)\widetilde{{\cal T}}(S)
by shift coordinates equips this space with a natural polyhedral structure, which we describe more precisely as a cone over
an octahedron in
\Bbb R3{\Bbb {R}}^3
. Each cone over a simplex of this octahedron is interpreted as a Teichmüller space of the sphere with
\frak b{\frak b}
boundary components and
\frak p{\frak p}
cusps, for fixed
\frak b{\frak b}
and
\frak p{\frak p}
, the sphere being furthermore equipped with an orientation on each boundary component. There is a natural linear action of
a finite group on
[(T)\tilde](S)\widetilde{{\cal T}}(S)
whose quotient is an augmented Teichmüller space in the usual sense. We describe several aspects of the geometry of the space
[(T)\tilde](S)\widetilde{{\cal T}}(S)
. Stretch lines and earthquakes can be defined on this space. In the second part of the paper, we use the shift coordinates
to obtain estimates on the behaviour of stretch lines in the Teichmüller space of a surface obtained by gluing hyperbolic
pairs of pants. We also use the shift coordinates to give formulae that express stretch lines in terms of Fenchel-Nielsen
coordinates. We deduce the disjointness of some stretch lines in Teichmüller space. We study in more detail the case of a
closed surface of genus 2. 相似文献
14.
B.-Y. Chen 《Archiv der Mathematik》2000,74(2):154-160
Let M n be a Riemannian n-manifold. Denote by S(p) and [`(Ric)](p)\overline {Ric}(p) the Ricci tensor and the maximum Ricci curvature on M n at a point p ? Mnp\in M^n, respectively. First we show that every isotropic submanifold of a complex space form [(M)\tilde]m(4 c)\widetilde M^m(4\,c) satisfies S £ ((n-1)c+ [(n2)/4] H2)gS\leq ((n-1)c+ {n^2 \over 4} H^2)g, where H2 and g are the squared mean curvature function and the metric tensor on M n, respectively. The equality case of the above inequality holds identically if and only if either M n is totally geodesic submanifold or n = 2 and M n is a totally umbilical submanifold. Then we prove that if a Lagrangian submanifold of a complex space form [(M)\tilde]m(4 c)\widetilde M^m(4\,c) satisfies [`(Ric)] = (n-1)c+ [(n2)/4] H2\overline {Ric}= (n-1)c+ {n^2 \over 4} H^2 identically, then it is a minimal submanifold. Finally, we describe the geometry of Lagrangian submanifolds which satisfy the equality under the condition that the dimension of the kernel of second fundamental form is constant. 相似文献
15.
Linear Complementarity Problems (LCPs) belong to the class of
\mathbbNP{\mathbb{NP}} -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which,
according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of
the original problem or detects the lack of property P*([(k)\tilde]){\mathcal{P}_*(\tilde\kappa)} , with arbitrary large, but apriori fixed [(k)\tilde]{\tilde\kappa}). In the latter case, the algorithms give a polynomial size certificate depending on parameter [(k)\tilde]{\tilde{\kappa}} , the initial interior point and the input size of the LCP). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following
interior point algorithms. 相似文献
16.
We show that, for a rationally inessential orientable closed n-manifold M whose fundamental group is a duality group, the macroscopic dimension of its universal cover [(M)\tilde]\tilde M is strictly less than n: dim
MC
[(M)\tilde] < n\tilde M < n. As a corollary, we obtain the following partial result towards Gromov’s conjecture 相似文献
17.
The problem of minimizing [(f)\tilde]=f+p{\tilde f=f+p} over some convex subset of a Euclidean space is investigated, where f(x) = x
T
Ax + b
T
x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function [(f)\tilde]{\tilde f} is strictly outer γ-convex for any γ > γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of [(f)\tilde]{\tilde f} is its global minimal solution and the diameter of the set of global minimal solutions of [(f)\tilde]{\tilde f} is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of [(f)\tilde]{\tilde f} is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of [(f)\tilde]{\tilde f} and some generalized optimality conditions. 相似文献
18.
We establish two new lower bounds for the halfspace range searching problem: Given a set of n points in ℝ
d
, where each point is associated with a weight from a commutative semigroup, compute the semigroup sum of the weights of the
points lying within any query halfspace. Letting m denote the space requirements, we prove a lower bound for general semigroups of
[\varOmega\tilde](n1-1/(d+1)/m1/(d+1))\widetilde{\varOmega}(n^{1-1/(d+1)}/m^{1/(d+1)}) and for integral semigroups of
[\varOmega\tilde](n/m1/d)\widetilde{\varOmega}(n/m^{1/d}). 相似文献
19.
In this paper, we reprove that: (i) the Aluthge transform of a complex symmetric operator
[(T)\tilde] = |T|\frac12 U|T|\frac12\tilde{T} = |T|^{\frac{1}{2}} U|T|^{\frac{1}{2}} is complex symmetric, (ii) if T is a complex symmetric operator, then ([(T)\tilde])*(\tilde{T})^{*} and [(T*)\tilde]\widetilde{T^{*}} are unitarily equivalent. And we also prove that: (iii) if T is a complex symmetric operator, then [((T*))\tilde]s,t\widetilde{(T^{*})}_{s,t} and ([(T)\tilde]t,s)*(\tilde{T}_{t,s})^{*} are unitarily equivalent for s, t > 0, (iv) if a complex symmetric operator T belongs to class wA(t, t), then T is normal. 相似文献
20.
A. V. Kartashova 《Journal of Mathematical Sciences》2009,163(6):682-687
In this paper, it is shown that the dual
[(\textQord)\tilde]\mathfrakA \widetilde{\text{Qord}}\mathfrak{A} of the quasiorder lattice of any algebra
\mathfrakA \mathfrak{A} is isomorphic to a sublattice of the topology lattice
á( \mathfrakA ) \Im \left( \mathfrak{A} \right) . Further, if
\mathfrakA \mathfrak{A} is a finite algebra, then
[(\textQord)\tilde]\mathfrakA @ á( \mathfrakA ) \widetilde{\text{Qord}}\mathfrak{A} \cong \Im \left( \mathfrak{A} \right) . We give a sufficient condition for the lattices
[(\textCon)\tilde]\mathfrakA\text, [(\textQord)\tilde]\mathfrakA \widetilde{\text{Con}}\mathfrak{A}{\text{,}} \widetilde{\text{Qord}}\mathfrak{A} , and
á( \mathfrakA ) \Im \left( \mathfrak{A} \right) . to be pairwise isomorphic. These results are applied to investigate topology lattices and quasiorder lattices of unary algebras. 相似文献
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