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1.
We study hypersurfaces in Euclidean space
whose position vector x satisfies the condition L
k
x = Ax + b, where L
k
is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed
,
is a constant matrix and
is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature and open pieces of round hyperspheres and generalized right spherical cylinders of the form
, with
. This extends a previous classification for hypersurfaces in
satisfying
, where
is the Laplacian operator of the hypersurface, given independently by Hasanis and Vlachos [J. Austral. Math. Soc. Ser. A
53, 377–384 (1991) and Chen and Petrovic [Bull. Austral. Math. Soc. 44, 117–129 (1991)].
相似文献
2.
Yuan Zhang 《Mathematische Annalen》2007,337(2):457-478
Let
and
denote the complexifications of Heisenberg hypersurfaces in
and
, respectively. We show that non-degenerate holomorphic Segre mappings from
into
with
possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from
into
with
propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2. 相似文献
3.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
4.
We compute the and monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we
provide a proof that the monodromy of the moduli space of hyperelliptic curves of genus g is the symplectic group . We prove that the monodromy of the moduli space of trielliptic curves with signature (r,s) is the special unitary group .
Rachel Pries was partially supported by NSF grant DMS-04-00461. 相似文献
5.
Tyler Lawson 《K-Theory》2006,37(4):395-422
For finitely generated groups G and H, we prove that there is a weak equivalence
G H (G × H) of ku-algebra spectra, where denotes the “unitary deformation K-theory” functor. Additionally, we give spectral sequences for computing the homotopy groups of G and HG in terms of connective K-theory and homology of spaces of G-representations. 相似文献
6.
In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter
semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C
0-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X
2) is T(t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C
0-semigroup even in the general case where the kernel of the dichotomic projector, X
2, is not assumed to be T(t)-invariant.
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7.
Jean-Christophe Bourgoin 《Annals of Global Analysis and Geometry》2007,32(1):1-13
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E
f,p
among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst.
Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real with , the map minimizes E
f,p
among the maps in which coincide with on .
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8.
Yehuda Pinchover Kyril Tintarev 《Calculus of Variations and Partial Differential Equations》2007,28(2):179-201
Let Ω be a domain in , d ≥ 2, and 1 < p < ∞. Fix . Consider the functional Q and its Gateaux derivative Q′ given by If Q ≥ 0 on, then either there is a positive continuous function W such that for all, or there is a sequence and a function v > 0 satisfying Q′ (v) = 0, such that Q(u
k
) → 0, and in . In the latter case, v is (up to a multiplicative constant) the unique positive supersolution of the equation Q′ (u) = 0 in Ω, and one has for Q an inequality of Poincaré type: there exists a positive continuous function W such that for every satisfying there exists a constant C > 0 such that . As a consequence, we prove positivity properties for the quasilinear operator Q′ that are known to hold for general subcritical resp. critical second-order linear elliptic operators. 相似文献
9.
Juan A. Aledo José M. Espinar José A. Gálvez 《Calculus of Variations and Partial Differential Equations》2007,29(3):347-363
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces and . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature
c > 0 into and a unique one into when c > 1, up to isometries of the ambient space. Moreover, we show that the hyperbolic plane of constant curvature c < −1 cannot be isometrically immersed into or .
J.A. Aledo was partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746 and Junta de Comunidades de
Castilla-La Mancha, grant no. PAI-05-034.
J.M. Espinar and J.A. Gálvez were partially supported by Ministerio de Education y Ciencia grant no. MTM2004-02746 and Junta
de Andalucía Grant No. FQM325. 相似文献
10.
In this paper, we characterize the dynamic of every Abelian subgroups
of
,
or
. We show that there exists a
-invariant, dense open set U in
saturated by minimal orbits with
a union of at most n
-invariant vector subspaces of
of dimension n−1 or n−2 over
. As a consequence,
has height at most n and in particular it admits a minimal set in
.
This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15 相似文献
11.
Bing Ye Wu 《Annals of Global Analysis and Geometry》2007,31(4):375-384
Let
be a Minkowski 3-space of Randers type with
, where
is the Euclidean metric and
. We consider minimal surfaces in
and prove that if a connected surface M in
is minimal with respect to both the Busemann–Hausdorff volume form and the Holmes–Thompson volume form, then up to a parallel
translation of
, M is either a piece of plane or a piece of helicoid which is generated by lines screwing about the x
3-axis.
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12.
Let denote the set of simultaneously - approximable points in and denote the set of multiplicatively ψ-approximable points in . Let be a manifold in . The aim is to develop a metric theory for the sets and analogous to the classical theory in which is simply . In this note, we mainly restrict our attention to the case that is a planar curve . A complete Hausdorff dimension theory is established for the sets and . A divergent Khintchine type result is obtained for ; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on of is full. Furthermore, in the case that is a rational quadric the convergent Khintchine type result is obtained for both types of approximation. Our results for
naturally generalize the dimension and Lebesgue measure statements of Beresnevich et al. (Mem AMS, 179 (846), 1–91 (2006)). Moreover, within the multiplicative framework, our results for constitute the first of their type.
The research of Victor V. Beresnevich was supported by an EPSRC Grant R90727/01. Sanju L. Velani is a Royal Society University
Research Fellow.
For Iona and Ayesha on No. 3. 相似文献
13.
Mika Hujo 《Journal of Theoretical Probability》2006,19(1):190-203
For a Borel-function
, we consider the approximation of a random variable f(W
1) with
by stochastic integrals with respect to the Brownian motion
and the geometric Brownian motion, where the integrands are piecewise constant within certain deterministic time intervals. In earlier papers it has been shown that under certain regularity conditions the optimal approximation rate is 1/
, if one optimizes over deterministic time-nets of cardinality n. We will show the existence of random variables f(W
1) such that the approximation error tends as slowly to zero as one wishes. 相似文献
14.
Michael Struwe 《Mathematische Zeitschrift》2007,256(2):397-424
For concentrating solutions weakly in H
2(Ω) to the equation on a domain with Navier boundary conditions the concentration energy is shown to be strictly quantized in multiples of the number . 相似文献
15.
Peter L. Søndergaard 《Advances in Computational Mathematics》2007,27(4):355-373
By sampling the window of a Gabor frame for belonging to Feichtinger’s algebra, , one obtains a Gabor frame for . In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations
among Gabor frames for the four spaces , , and . Some new results about general dual windows with respect to sampling and periodization are presented as well. This theory
is used to show a new result of the Kaiblinger type to construct an approximation to the canonical dual window of a Gabor
frame for .
相似文献
16.
Robert Černý 《Calculus of Variations and Partial Differential Equations》2007,28(2):203-216
We compute the relaxation
where
for sequences of functions from
converging strongly in the
-norm to
. 相似文献
17.
Marek Omelka 《Annals of the Institute of Statistical Mathematics》2007,59(2):385-402
The rank statistic
, with R
i
(t) being the rank of
and e
1
, . . . , e
n
being the random sample from a distribution with a cdf F, is considered as a random process with t in the role of parameter. Under some assumptions on c
i
, x
i
and on the underlying distribution, it is proved that the process
converges weakly to the Gaussian process. This generalizes the existing results where the one-dimensional case
was considered. We believe our method of the proof can be easily modified for the signed-rank statistics of Wilcoxon type.
Finally, we use our results to find the second order asymptotic distribution of the R-estimator based on the Wilcoxon scores and also to investigate the length of the confidence interval for a single parameter
β
l
. 相似文献
18.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu
.
Then
where
q is the set of q-multiplicative functions g such that . 相似文献
19.
Concettina Galati 《Annali di Matematica Pura ed Applicata》2009,188(2):359-368
Let be the variety of irreducible sextics with six cusps as singularities. Let be one of irreducible components of . Denoting by the space of moduli of smooth curves of genus 4, we consider the rational map sending the general point [Γ] of Σ, corresponding to a plane curve , to the point of parametrizing the normalization curve of Γ. The number of moduli of Σ is, by definition the dimension of Π(Σ). We know that
, where ρ(2, 4, 6) is the Brill–Noether number of linear series of dimension 2 and degree 6 on a curve of genus 4. We prove that both
irreducible components of have number of moduli equal to seven.
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20.
For a given map
defined on the field
of p-adic numbers satisfying
for some integer r, a Markov process on
induced by the map ϕ is constructed in (Kaneko and Zhao (1994) Forum Math. J. 16, 69). This approach can still be our choice in constructing a Markov process on finite algebraic extension of
. We will give an answer to the question as to how Markov process driven by set of maps will be addressed. Especially, we will focus on case the maps are given by the elements of Galois group of the extension. 相似文献