scholarly journals Ul’yanov-type inequality for bounded convex sets in Rd

2008 ◽  
Vol 151 (1) ◽  
pp. 60-85 ◽  
Author(s):  
Z. Ditzian ◽  
A. Prymak
Keyword(s):  
Convex Sets ◽  
Type Inequality ◽  
Bounded Convex

scholarly journals About an Erdős–Grünbaum Conjecture Concerning Piercing of Non-bounded Convex Sets

2015 ◽  
Vol 53 (4) ◽  
pp. 941-950
Author(s):  
Amanda Montejano ◽  
Luis Montejano ◽  
Edgardo Roldán-Pensado ◽  
Pablo Soberón
Keyword(s):  
Convex Sets ◽  
Bounded Convex

On the Vector Sum of Two Convex Sets in Space

1991 ◽  
Vol 43 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Steven G. Krantz ◽  
Harold R. Parks
Keyword(s):  
Convex Sets ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Vector Sum ◽  
Bounded Convex

In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

A classification for non-linearly bounded convex sets

1993 ◽  
Vol 61 (6) ◽  
pp. 576-583
Author(s):  
J. Bair ◽  
J. L. Valein
Keyword(s):  
Convex Sets ◽  
Bounded Convex

Order cancellation law in the family of bounded convex sets

2019 ◽  
Vol 77 (2) ◽  
pp. 289-300
Author(s):  
J. Grzybowski ◽  
R. Urbański
Keyword(s):  
Convex Sets ◽  
The Family ◽  
Bounded Convex

scholarly journals The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets

2013 ◽  
Vol 5 (1) ◽  
pp. 44-46
Author(s):  
I. Hetman
Keyword(s):  
Normed Space ◽  
Convex Sets ◽  
Infinite Dimensional ◽  
Dimensional Normed Space ◽  
Bounded Convex ◽  
Convex Subsets

We prove that an infinite-dimensional normed space $X$ is complete if and only if the space $\mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ is topologically homogeneous.

scholarly journals A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

2020 ◽  
Author(s):  
Simone Cito ◽  
Domenico Angelo La Manna
Keyword(s):  
Convex Sets ◽  
Type Inequality ◽  
First Eigenvalue ◽  
Type Problem ◽  
Laplacian Eigenvalue ◽  
Quantitative Form ◽  
Boundary Parameter ◽  
Robin Laplacian ◽  
Krahn Inequality ◽  
Optimal Set

The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalue λ β with negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer for λ β and the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.

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