共查询到20条相似文献,搜索用时 72 毫秒
1.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
2.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献
3.
Peng Zhu 《Archiv der Mathematik》2011,97(3):271-279
We prove that a complete noncompact orientable stable minimal hypersurface in
\mathbbSn+1{\mathbb{S}^{n+1}} (n ≤ 4) admits no nontrivial L
2-harmonic forms. We also obtain that a complete noncompact strongly stable hypersurface with constant mean curvature in
\mathbbRn+1{\mathbb{R}^{n+1}} or
\mathbbSn+1{\mathbb{S}^{n+1}} (n ≤ 4) admits no nontrivial L
2-harmonic forms. These results are generalized versions of Tanno’s result on stable minimal hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}}. 相似文献
4.
We consider the Radon transform on the (flat) torus
\mathbbTn = \mathbbRn/\mathbbZn{\mathbb{T}^{n} = \mathbb{R}^{n}/\mathbb{Z}^n} defined by integrating a function over all closed geodesics. We prove an inversion formula for this transform and we give
a characterization of the image of the space of smooth functions on
\mathbbTn{\mathbb{T}^{n}} . 相似文献
5.
We extend the theorem of B. Daniel about the existence and uniqueness of immersions into
\mathbbSn × \mathbbR or \mathbbHn × \mathbbR{\mathbb{S}^{n}\,\times\,\mathbb{R}\, {\rm or}\, \mathbb{H}^{n}\,\times\,\mathbb{R}} to the Riemannian product of two space forms. More precisely, we prove the existence and uniqueness of an isometric immersion
of a Riemannian manifold into the Riemannian product of two space forms. 相似文献
6.
The field of quaternions, denoted by
\mathbbH{\mathbb{H}} can be represented as an isomorphic four dimensional subspace of
\mathbbR4×4{\mathbb{R}^{4\times 4}}, the space of real matrices with four rows and columns. In addition to the quaternions there is another four dimensional
subspace in
\mathbbR4×4{\mathbb{R}^{4\times 4}} which is also a field and which has – in connection with the quaternions – many pleasant properties. This field is called
field of pseudoquaternions. It exists in
\mathbbR4×4{\mathbb{R}^{4\times 4}} but not in
\mathbbH{\mathbb{H}}. It allows to write the quaternionic linear term axb in matrix form as Mx where x is the same as the quaternion x only written as a column vector in
\mathbbR4{\mathbb{R}^4}. And M is the product of the matrix associated with the quaternion a with the matrix associated with the pseudoquaternion b. 相似文献
7.
Vladimir Tkachev 《Complex Analysis and Operator Theory》2010,4(3):685-700
In this paper, we construct two infinite families of algebraic minimal cones in
^n{\mathbb{R}^{n}}. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes
of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a
byproduct, we prove that for any n ≥ 4, n ≠ 16k + 1, there is at least one minimal cone in
\mathbbRn{\mathbb{R}^{n}} given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in
\mathbbRm2{\mathbb{R}^{m^2}}, m ≥ 2, defined by an irreducible homogeneous polynomial of degree m. These examples provide particular answers to the questions on algebraic minimal cones in
\mathbbRn{\mathbb{R}^{n}} posed by Wu-Yi Hsiang in the 1960s. 相似文献
8.
In this study, we obtain some Korovkin type approximation theorems by positive linear operators on the weighted space of all
real valued functions defined on the real two-dimensional Euclidean space
\mathbbR2{\mathbb{R}^2}. This paper is mainly consisted of two parts: a Korovkin type approximation theorem via the concept of A-statistical convergence
and a Korovkin type approximation theorem via A{\mathcal {A}}-summability. 相似文献
9.
Extending a result of Meyer and Reisner (Monatsh Math 125:219–227, 1998), we prove that if
g: \mathbbR? \mathbbR+{g: \mathbb{R}\to \mathbb{R}_+} is a function which is concave on its support, then for every m > 0 and every
z ? \mathbbR{z\in\mathbb{R}} such that g(z) > 0, one has
ò\mathbbR g(x)mdxò\mathbbR (g*z(y))m dy 3 \frac(m+2)m+2(m+1)m+3, \int\limits_{\mathbb{R}} g(x)^mdx\int\limits_{\mathbb{R}} (g^{*z}(y))^m dy\ge \frac{(m+2)^{m+2}}{(m+1)^{m+3}}, 相似文献
10.
Matteo Dalla Riva Massimo Lanza de Cristoforis 《Complex Analysis and Operator Theory》2011,5(3):811-833
Let Ω
i
and Ω
o
be two bounded open subsets of
\mathbbRn{{\mathbb{R}}^{n}} containing 0. Let G
i
be a (nonlinear) map from
?Wi×\mathbbRn{\partial\Omega^{i}\times {\mathbb{R}}^{n}} to
\mathbbRn{{\mathbb{R}}^{n}} . Let a
o
be a map from ∂Ω
o
to the set
Mn(\mathbbR){M_{n}({\mathbb{R}})} of n × n matrices with real entries. Let g be a function from ∂Ω
o
to
\mathbbRn{{\mathbb{R}}^{n}} . Let γ be a positive valued function defined on a right neighborhood of 0 in the real line. Let T be a map from
]1-(2/n),+¥[×Mn(\mathbbR){]1-(2/n),+\infty[\times M_{n}({\mathbb{R}})} to
Mn(\mathbbR){M_{n}({\mathbb{R}})} . Then we consider the problem
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