共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex
surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C1,α regularity for general domains and C1,1 regularity if the domain is uniformly convex.
This work is supported by the Australian Research Council. Research of Sheng was also supported by ZNSFC No. 102033.
On leave from Zhejiang University. 相似文献
2.
V. A. Toponogov 《Siberian Mathematical Journal》1994,35(4):815-817
The research was supported by the Russian Foundation for Fundamental Research (Grant 93-011-179). 相似文献
3.
Motivated by a conjecture of Steinhaus, we consider the mapping F, associating to each point x of a convex hypersurface the set of all points at maximal intrinsic distance from x. We first provide two large classes of hypersurfaces with the mapping F single-valued and involutive. Afterwards we show that a convex body is smooth and has constant width if its double has the above properties of F, and we prove a partial converse to this result. Additional conditions are given, to characterize the (doubly covered) balls. 相似文献
4.
Giorgio Patrizio 《manuscripta mathematica》1984,47(1-3):271-309
Using results of L. Lempert, we are able to construct parabolic exhaustions for strictly convex domains Dm with center at any given point of D. Using the theory of parabolic spaces and the geometric properties of these exhaustions, we can characterize the strictly convex domains biholomorphic to a circular domain and in particular to the ball in m.Supported by a grant from the C.N.R. (Italy) 相似文献
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Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions.
The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair
of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative
internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm
— are presented.
This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l. 相似文献
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8.
Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions. The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative internal tactics for the dual problem are examined. Computational experiments — aimed at the improved efficiency of the algorithm — are presented.This research was supported in part by National Science Foundation Grant No. DCR-8401098-A01. 相似文献
9.
BIT Numerical Mathematics - In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well-known... 相似文献
10.
周家足 《数学物理学报(B辑英文版)》2011,31(2):361-366
Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere. 相似文献
11.
A. D. Milka 《Journal of Mathematical Sciences》1986,33(2):910-933
We give a survey of results of the author on the geometry of geodesics and shortest curves on general convex hypersurfaces in spaces with constant curvature. We present qualitatively new theorems, which unite and generalize the main classical results; we give applications to the solution of a number of actual problems of geometry of convex surfaces in the large. We give generalizations of some well-known theorems on geodesics and shortest curves to Riemannian manifolds and nonregular multidimensional convex metrics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 16, pp. 155–194, 1984. 相似文献
12.
Ben Andrews James McCoy Yu Zheng 《Calculus of Variations and Partial Differential Equations》2013,47(3-4):611-665
We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after finite time. The same holds if the initial data is only weakly convex or non-smooth, and the limiting shape at the final time is spherical. We provide a surprisingly large family of flows for which such results fail, by a variety of mechanisms: Uniformly convex hypersurfaces may become non-convex, and smooth ones may develop curvature singularities; even where this does not occur, non-uniformly convex regions and singular parts in the initial hypersurface may persist, including flat sides, ridges of infinite curvature, or ‘cylindrical’ regions where some of the principal curvatures vanish; such cylindrical regions may persist even if the speed is positive, and in such cases the hypersurface may even collapse to a line segment or higher-dimensional disc rather than to a point. We provide sufficient conditions for these various disasters to occur, and by avoiding these arrive at a class of flows for which arbitrary weakly convex initial hypersurfaces immediately become smooth and uniformly convex and contract to points. 相似文献
13.
Pak Tung Ho 《Differential Geometry and its Applications》2008,26(3):273-276
Suppose that M is a compact orientable hypersurface embedded in a compact n-dimensional orientable Riemannian manifold N. Suppose that the Ricci curvature of N is bounded below by a positive constant k. We show that 2λ1>k−(n−1)maxM|H| where λ1 is the first eigenvalue of the Laplacian of M and H is the mean curvature of M. 相似文献
14.
An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n+1)-space is Euclidean complete for n≥2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface
in R
3 must be an elliptic paraboloid.
Oblatum 16-VI-2001 & 27-II-2002?Published online: 29 April 2002 相似文献
15.
Tudor Zamfirescu 《Monatshefte für Mathematik》1987,103(1):57-62
By an old result of Klee, those convex bodies which are not smooth or not strictly convex form a set of first Baire category. It is proved here that they are “even fewer”: they only form a σ-porous set. 相似文献
16.
Maxim V. Balashov 《Journal of Mathematical Analysis and Applications》2011,374(2):529-537
We consider polyhedral approximations of strictly convex compacta in finite-dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls. 相似文献
17.
Sabine Dieter 《Calculus of Variations and Partial Differential Equations》2005,22(2):229-251
We study the evolution of closed, weakly convex hypersurfaces in
in direction of their normal vector, where the speed equals a quotient of successive elementary symmetric polynomials of the principal curvatures. We show that there exists a solution for these weakly convex surfaces at least for some short time if the elementary symmetric polynomial in the denominator of the quotient is positive. The results for this nonlinear, degenerate flow are obtained by a cylindrically symmetric barrier construction.Received: 10 November 2003, Accepted: 5 April 2004, Published online: 16 July 2004 相似文献
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In this paper we derive a sharp estimate for the supremum of the scalar curvature (or, equivalently, the infimum of the squared
norm of the second fundamental form) of a constant mean curvature hypersurface with two principal curvatures immersed into
a Riemannian space form of constant curvature. Our results will be an application of the generalized Omori-Yau maximum principle,
following the approach by Pigola et al. (Memoirs Am Math Soc 822, 2005). 相似文献