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1.
Felix Finster Oliver C. Schnürer 《Calculus of Variations and Partial Differential Equations》2002,15(1):67-80
We prove an existence theorem for convex hypersurfaces of prescribed Gau? curvature in the complement of a compact set in
Euclidean space which are close to a cone.
Received: 23 February 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献
2.
In this paper we give a conformal representation of flat surfaces in the hyperbolic 3-space using the complex structure induced
by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends.
Received: 18 September 1997 相似文献
3.
Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric
deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property.
We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that
isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional
generalizations of constant mean curvature surfaces which are K?hler submanifolds with parallel (1,1) part of their soecond
fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family.
Examples where this family is constant arise from extrinsic K?hler symmetric spaces.
Received: 8 July 1997 相似文献
4.
5.
The aim of this paper is to study the moduli space of solutions of the Dirichlet problem associated to the equation of Monge-Ampeère
type, det , on an exterior planar domain. We prove that this moduli space is either empty or a differentiable manifold of dimension
five.
(Received 23 April 1999) 相似文献
6.
史淑国 《数学年刊A辑(中文版)》2001,(6)
首先叙述双曲空间中曲面的Gauss映照的定义;导出Gauss映照所满足的Beltrami方程;给出了给定平均曲率曲面的Weierstrass表示公式;并讨论了这种表示的完全可积条件. 相似文献
7.
Ulrich Clarenz Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2001,12(1):85-107
We consider parametric variational double integrals with elliptic Lagrangians F depending on the surface normal and prove a compactness theorem for -critical immersions. As a key ingredient for the relevant a priori estimates we use F. Sauvigny's F-conformal parameters adapted to the parametric integrand F. As a by-product of our analysis we obtain an isoperimetric inequality for -critical immersions generalizing the classical isoperimetric inequality for minimal surfaces.
Received November 19, 1999 / Accepted February 4, 2000 / Published online July 20, 2000 相似文献
8.
We study complete minimal surfaces M immersed in R
3, with finite topology and one end. We give conditions which oblige M to be conformally a compact Riemann surface punctured in one point, and we show that M can be parametrized by meromorphic data on this compact Riemann surface. The goal is to prove that when M is also embedded, then the end of M is asymptotic to an end of a helicoid (or M is a plane).
Received: 13 January 1997 / Revised version: 15 September 1997 相似文献
9.
Mappings of finite distortion: Monotonicity and continuity 总被引:10,自引:0,他引:10
10.
Jun Ai Kai-Seng Chou Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2001,13(3):311-337
Similarity between the roles of the group on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group
of on the Nirenberg problem for prescribed scalar curvature is explored. Sufficient conditions for the existence of affine self-similar
curves are established.
Received June 26, 1999 / Accepted January 28, 2000 / Published online December 8, 2000 相似文献
11.
The uniqueness of stable ultimate shapes for the generalized curve-shortening problem is established for a class of anisotropic factors. Received: 24 June 1999 相似文献
12.
R. Aiyama K. Akutagawa 《Calculus of Variations and Partial Differential Equations》2002,14(4):399-428
The purpose of this paper is to study some uniqueness, existence and regularity properties of the Dirichlet problem at infinity
for proper harmonic maps from the hyperbolic m-space to the open unit n-ball with a specific incomplete metric. When m=n=2, harmonic solutions of this Dirichlet problem yield complete constant mean curvature surfaces in the hyperbolic 3-space.
Received: 25 January 2001 / Accepted: 23 February 2001 / Published online: 25 June 2001 相似文献
13.
14.
The concept of harmonic pseudo-horizontally homothetic submersion, alias harmonic PHH submersion, expresses the more geometric notion of smooth family of minimal submanifolds indexed by a K?hler parameter manifold. We
give results that allow to construct harmonic PHH submersions by solving some implicit equations and we apply this method
to the case of sphere bundles.
Received: 3 September 1998 / Accepted: 19 March 1999 相似文献
15.
16.
《偏微分方程通讯》2013,38(5-6):1103-1137
ABSTRACT We study the coupled Navier-Stokes Ginzburg-Landau model of nematic liquid crystals introduced by F.H. Lin, which is a simplified version ofthe Ericksen-Leslie system. We generalize the model to compact n-dimensional Riemannian manifolds, deriving the system from a variational principle, and provide a very simple proof of local well-posedness for this coupled system using a contraction mapping argument. We then prove that this system is globally well-posed and has compact global attractors when the dimension of the manifold M is two. A small data result in n dimensions follows easily. Finally, we introduce the Lagrangian averaged liquid crystal equations, which arise from averaging the Navier-Stokes fluid motion over small spatial scales in the variational principle. We show that this averaged system is globally well-posed and has compact global attractors even when M is three-dimensional. 相似文献
17.
The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation
{△^2u + a(x)u = g(x, u)
u∈ H^2(R^N),
where the condition u∈ H^2(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. 相似文献
{△^2u + a(x)u = g(x, u)
u∈ H^2(R^N),
where the condition u∈ H^2(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. 相似文献
18.
Gilles Carron 《Mathematische Annalen》1999,314(4):613-639
Sans résumé
Received: 15 May 1997 / in final form: 5 February 1998 相似文献
19.
20.
In this paper, we prove the validity of the Chern conjecture in affine geometry [18], namely that an affine maximal graph
of a smooth, locally uniformly convex function on two dimensional Euclidean space, R
2, must be a paraboloid. More generally, we shall consider the n-dimensional case, R
n
, showing that the corresponding result holds in higher dimensions provided that a uniform, “strict convexity” condition holds.
We also extend the notion of “affine maximal” to non-smooth convex graphs and produce a counterexample showing that the Bernstein
result does not hold in this generality for dimension n≥10.
Oblatum 16-IV-1999 & 4-XI-1999?Published online: 21 February 2000 相似文献