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1.
Albert Borbély 《Journal of Geometry》1995,54(1-2):3-14
In Hadamard manifolds the existence of suitable large convex sets is important for solving the Dirichlet problem at infinity. In this note we proveC
1 boundary regularity of the convex hull of any compact setK away from points which lie on geodesics connecting points inK.The research was supported by the Hungarian Science Foundation Grant 4232 and by the Kuwait University Research Grant SM 080. 相似文献
2.
This paper deals with bounded linear regularity, linear regularity and the strong conical hull intersection property (CHIP)
of a collection of finitely many closed convex intersecting sets in Banach spaces. It is shown that, as in finite dimensional
space setting (see [6]), the standard constraint qualification implies bounded linear regularity, which in turn yields the
strong conical hull intersection property, and that the collection of closed convex sets {C
1, . . . ,C
n
} is bounded linearly regular if and only if the tangent cones of {C
1, . . . ,C
n
} has the CHIP and the normal cones of {C
1, . . . ,C
n
} has the property (G)(uniformly on a neighborhood in the intersection C). As applications, we study the global error bounds for systems of linear and convex inequalities.
The work of this author was partially supported by the National Natural Sciences Grant (No. 10471032) and the Excellent Young
Teachers Program of MOE, P.R.C
The authors thank professor K.F.Ng for his helpful discussion and the referee for their helpful suggestions on improving the
first version of this paper 相似文献
3.
Roswitha Blind 《manuscripta mathematica》1977,21(3):243-253
It is well known, that in E3 the spheres are the closed convex C2 -surfaces having the property, that each of their closed C2-curves with the total geodesic curvature O bisects the area of the surface. This characterization will be transmitted into the theory of convex surfaces founded by A.D.Alexandrov, where convex surfaces without any differentiability property are studied. 相似文献
4.
Abstract
In this paper, we construct first a new concrete example
of asymmetric convex compact C
1,1-hypersurfaces
in R
2n
possessing precisely n
closed characteristics. Then we prove multiplicity results on
the closed characteristics on convex compact hypersurfaces in
R
2n
pinched by not
necessarily symmetric convex compact hypersurfaces.
*Partially supported by the 973 Program of STM,
Funds of EC of Jiangsu, the Natural Science Funds of Jiangsu (BK
2002023), the Post-doctorate Funds of China, and the NNSF of
China (10251001)
**Partially supported by the 973 Program of STM,
NNSF, MCME, RFDP, PMC Key Lab of EM of China, S. S. Chern
Foundation, and Nankai University 相似文献
5.
T. Rapcsák 《Journal of Optimization Theory and Applications》1991,69(1):169-183
The properties of geodesic convex functions defined on a connected RiemannianC
2
k-manifold are investigated in order to extend some results of convex optimization problems to nonlinear ones, whose feasible region is given by equalities and by inequalities and is a subset of a nonlinear space.This research was supported in part by the Hungarian National Research Foundation, Grant No. OTKA-1044. 相似文献
6.
Franz Aurenhammer 《Discrete and Computational Geometry》1987,2(1):49-64
A criterion is given that decides, for a convex tilingC ofR
d
, whetherC is the projection of the faces in the boundary of some convex polyhedronP inR
d+1. Its applicability is restricted neither by the properties nor by the dimension ofC. It turns out to be conceptually simpler than other criteria and allows the easy examination of various classes of cell complexes. In addition, the criterion is constructive, that is, it can be used to constructP provided it exists.Research was supported by the Austrian Fonds zur Foerderung der wissenschaftlichen Forschung. 相似文献
7.
Univariate cubic L
1 smoothing splines are capable of providing shape-preserving C
1-smooth approximation of multi-scale data. The minimization principle for univariate cubic L
1 smoothing splines results in a nondifferentiable convex optimization problem that, for theoretical treatment and algorithm
design, can be formulated as a generalized geometric program. In this framework, a geometric dual with a linear objective
function over a convex feasible domain is derived, and a linear system for dual to primal conversion is established. Numerical
examples are given to illustrate this approach. Sensitivity analysis for data with uncertainty is presented.
This work is supported by research grant #DAAG55-98-D-0003 of the Army Research Office, USA. 相似文献
8.
Jiguang Bao 《中国科学A辑(英文版)》1998,41(10):1047-1050
Under the mild conditions, it is proved that the convex surface is global C1.1, with the given Gaussian curvature 0≤K ∈ C
0
∞
and the given boundary curve. Examples are given to show that the regularity is optimal.
Project supported by the Doctoral Funds of China and the National Natural Science Foundation of China (Grant No. 19771009). 相似文献
9.
We prove a generalization of the 4 vertex theorem forC
3 closed simple convex space curves including singular and zero curvature points.Work partially supported by CNPq. The second author is also grateful to the Universidade Federal de Viçosa (Brasil) for hospitality during the production of this work. 相似文献
10.
In this paper, we present second-order optimality conditions for convex composite minimization problems in which the objective function is a composition of a finite-valued or a nonfinite-valued lower semicontinuous convex function and aC
1,1 function. The results provide optimality conditions for composite problems under reduced differentiability requirements.This paper is a revised version of the Departmental Preliminary Report AM92/32, School of Mathematics, University of New South Wales, Kensington, NSW, Australia.Research of this author was supported in part by an Australian Research Council Grant. 相似文献
11.
Lawrence C. Evans Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2008,32(3):325-347
We propose a new method for showing C
1, α
regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The
proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.
LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in
Science, Berkeley. 相似文献
12.
M. Edelstein 《Israel Journal of Mathematics》1969,7(1):90-94
LetA be a finite nonempty family of nonempty disjoint closed and bounded sets in a Banach spaceE which is either separable and the conjugate of some Banach spaceX (i.e.E=X*) or, reflexive and locally uniformly convex. IfC denotes the weak*-closed convex hull of ∪ {A:A ∈A} then the set of points inE ∼C through which there is no hyperplane intersecting exactly one member ofA is discrete (or empty).
This research was supported by the National Research Council of Canada, Grant A-3999. 相似文献
13.
Rolf Schneider 《manuscripta mathematica》1990,69(1):291-300
In the quadratic Aleksandrov-Fenchel inequality for mixed volumes, stated as inequality (1) below, whereC
1, ...,C
n-2 are smooth convex bodies, equality holds only if the convex bodiesK andL are homothetic. Under stronger regularity assumptions onC
1,...,C
n-2, a stability estimate is proved, expressing thatK andL are close to homothetic if equality is satisfied approximately. This is applied to estimate explicitly the deviation of a
closed convex hypersurface with mean curvature close to one from a unit sphere. 相似文献
14.
We prove a closed graph theorem for Baire locally convex spaces (for Baire linear topological spaces) in the domain and weakly C‐Suslin locally convex spaces (respectively, for C‐Suslin linear topological spaces) in the range which improves some classic closed graph theorems and other, more recent, related results. 相似文献
15.
An efficient approach to computing the convex best C
1-spline interpolant to a given set of data is to solve an associated dual program by standard numerical methods (e.g., Newton’s
method). We study regularity and well-posedness of the dual program: two important issues that have been not yet well-addressed
in the literature. Our regularity results characterize the case when the generalized Hessian of the objective function is
positive definite. We also give sufficient conditions for the coerciveness of the objective function. These results together
specify conditions when the dual program is well-posed and hence justify why Newton’s method is likely to be successful in
practice. Examples are given to illustrate the obtained results.
The work was supported by EPSRC grant EP/D502535/1 for the first author and by a grant from the Research Grants Council of
the Hong Kong Special Administrative Region, China (Project No. PolyU 5141/01E) for the second author. 相似文献
16.
Soon-Mo Jung 《Bulletin of the Brazilian Mathematical Society》2009,40(1):77-84
Let E
n
be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex
subset Co of E
n
into E
n
, preserves a distance ρ, then the restriction of f to an open convex subset C
∞ of C
0 is an isometry.
This work was supported by 2007 Hongik University Research Fund. 相似文献
17.
The structure of the groupoidG associated with the ToeplitzC
*-algebraC
*(Ω) of the L-shaped domain is discussed. The detailed characterization ofM
∞ by the classification of the closed subgroup of the Euclidean space is presented.
Project supported partially by the National Natural Science Foundation of China, Fok Yingtung Educational Foundation and the
Foundation of the State Education Commission of China. 相似文献
18.
We study the evolution of a closed, convex hypersurface in ℝn+1 in direction of its normal vector, where the speed equals a positive power k of the mean curvature. We show that the flow exists on a maximal, finite time interval, and that, approaching the final time,
the surfaces contract to a point.
The author was partially supported by a Schweizerische Nationalfonds grant No. 21-66743.01. 相似文献
19.
Sheng Zhi Zhu 《数学学报(英文版)》2010,26(8):1449-1456
We prove that the set of vector fields satisfying the C1 stable shadowable property on closed surfaces is characterized as the set of Morse-Smale vector fields. Hence, the vector fields satisfying shadowing property on closed surfaces are C1 dense. 相似文献
20.
Yu. É. Linke 《Mathematical Notes》1998,63(2):183-189
The existence of separately continuous selectors of a separately lower and upper semicontinuous many-valued multivariate map
is proved, provided its domain is a compact set and its range is a convex closed subset of a metrizable convex compact set.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 209–216, February, 1998.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 93-01-00264. 相似文献