A Note on Self-extremal Sets in $L_p(\Om)$ Spaces
英文摘要:
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.
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。
V. Nguyen-Khac, K. Nguyen-Van
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.
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
We find minimal and maximal length of intersections of lines at a fixed distance to the origin with the cross-polytope. We also find maximal volume noncentral sections of the cross-polypote by hyperplanes which are at a fixed large distance to the origin and minimal volume sections by symmetric slabs of a large fixed width. This parallels recent results about noncentral sections of the cube due to Moody, Stone, Zach and Zvavitch.
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.
We give a geometric characterization of extremal sets in ell_p spaces that generalizes our previous result for such sets in Hilbert spaces.
An almost Kähler structure is {\it extremal} if the Hermitian scalar curvature is a Killing potential [29]. When the almost complex structure is integrable it coincides with extremal Kähler metric in the sense of Calabi [8]. We observe that the existence of an extremal {\it toric} almost Kähler structure of involutive type implies uniform K-stability and we point out the existence of a formal solution of the Abreu equation for any angle along the invariant divisor. Applying the recent result of Chen--Cheng [10] and He [27], we conclude that the existence of a compatible extremal toric almost K…
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.
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。
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.
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…
In this note we investigate the behavior of the volume that the convex hull of two congruent and intersecting simplices in Euclidean $n$-space can have. We prove some useful equalities and inequalities on this volume. For the regular simplex we determine the maximal possible volume for the case when the two simplices are related to each other via reflection at a hyperplane intersecting them.
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。
Sampaio recently showed that bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones. The purpose of this note is to show that Sampaio's method works as well for (SSP) sets, that is, the above result is characteristic for (SSP) sets, a much wider class.
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。
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。