首页/论文/math/0203190

arXiv math/02031902002-03math.MGmath.FA

A Characterization of Extremal Sets in Hilbert Spaces

V. NguyenKhac, K. NguyenVan

备注：: 10 pages, corrected some misprints

英文摘要：

We give a characterization of extremal sets in Hilbert spaces that generalizes a classical theorem of H. W. E. Jung. We investigate also the behaviour of points near to the circumsphere of such a set with respect to the Kuratowski and Hausdorff measures of non-compactness.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A Geometric Characterization of Extremal Sets in ell_p Spaces

We give a geometric characterization of extremal sets in ell_p spaces that generalizes our previous result for such sets in Hilbert spaces.

2002-08-18math.FAmath.MG

A Note on Self-extremal Sets in $L_p(\Om)$ Spaces

We give a geometric characterization of self-extremal sets in $L_p(\Om)$ spaces that partially extends our previous results to the case of $L_p$\ spaces.

2004-11-25math.MG

Extremal elements in hypercomplex space

Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space are investigated. Introduced a class of H-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections.

2015-09-29math.MG

偏序集上 Stanley 不等式的极值情形

The extremals of Stanley's inequalities for partially ordered sets

本文完整刻画了偏序集上 Stanley 不等式的等号成立情形，通过建立偏序集组合学与凸多面体几何之间的新“字典”来刻画极值结构。

2023-11-30math.COmath.MG

Parkable convex sets and finite-dimensional Hilbert spaces

A subset of a convex body $B$ containing the origin in a Euclidean space is {\it parkable in $B$} if it can be translated inside $B$ in such a manner that the translate the origin. We provide characterizations of ellipsoids and of centrally symmetric convex bodies in Euclidean spaces of dimension $\ge 3$ based on the notion of parkability, answering several questions posed by G. Bergman. The techniques used, which are based on characterizations of Hilbert spaces among finite-dimensional Banach spaces in terms of their lattices of subspaces and algebras of endomorphisms, also apply to improve a…

2016-03-29math.FAmath.MG

Geometric properties of extremal sets for the dimension comparison in Carnot groups of step 2

In Carnot groups of step 2 we consider sets having maximal or minimal possible homogeneous Hausdorff dimension compared to their Euclidean one: in the first case we prove that they must be in a sense vertical, that is a large part of these sets can lie off horizontal planes through their points, and in the latter case close to horizontal. The examples that had been used to prove the sharpness of the sub-Riemannian versus Euclidean dimension comparison intuitively satisfied these geometric properties, which we here quantify and prove to be necessary. We also show the sharpness of our statements…

2018-08-30math.CAmath.MG

更多相关论文收起更多论文

复双曲空间中的四面体与具有Pick核的Hilbert空间

Tetrahedra in complex hyperbolic space and Hilbert spaces with Pick kernels

本文研究复双曲空间几何与完全Pick核Hilbert空间的关系，提出顶点角余弦的复模拟，用于描述四面体三角面及四维Pick核空间的三维子空间。

2020-03-25math.FAmath.GTmath.MG

极值几何中的锥优化

Conic optimization for extremal geometry

本文综述了锥优化在四种几何堆积问题（单位球面上的接吻数与可测π/2回避集，欧氏空间中的球堆积与可测一回避集）中的最新应用进展。

2025-10-08math.MGmath.OC

On the sum of powered distances to certain sets of points on the circle

In this paper we consider an extremal problem in geometry. Let $λ$ be a real number and $A$, $B$ and $C$ be arbitrary points on the unit circle $Γ$. We give full characterization of the extremal behavior of the function $f(M,λ)=MA^λ+MB^λ+MC^λ$, where $M$ is a point on the unit circle as well. We also investigate the extremal behavior of $\sum_{i=1}^nXP_i$, where $P_i, i=1,...,n$ are the vertices of a regular $n$-gon and $X$ is a point on $Γ$, concentric to the circle circumscribed around $P_1...P_n$. We use elementary analytic and purely geometric methods in the proof.

2011-08-23math.MG

关于单纯Tits集的Hilbert几何

On the Hilbert geometry of simplicial Tits sets

本文研究了单纯双曲Coxeter轨道流形上凸射影结构的模空间，证明了当模空间为实数轴且趋于无穷时，Hilbert度量的熵趋于0。

2014-07-11math.DGmath.MG

Sweeping process by prox-regular sets in Riemannian Hilbert manifolds

In this paper, we deal with sweeping processes on (possibly infinite-dimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of the ambient manifold and we check that this regularity implies a property of hypomonotonicity for the proximal normal cone. Moreover we show that the metric projection onto a locally prox-regular set is sin…

2015-01-28math.APmath.MG

Alexandrov空间是CS集

Alexandrov spaces are CS sets

本文证明了Alexandrov空间的极值分层是Siebenmann意义下的CS分层，并证明了无真极值子集的Alexandrov空间方向空间同胚于球面，多面体情形下该结论对迭代方向空间同样成立。

2025-08-11math.DGmath.GTmath.MG