scholarly journals Asymptotics of sharp constants in Markov–Bernstein–Nikolskii type inequalities with exponential weights

2021 ◽  
Vol 265 ◽  
pp. 105550
Author(s):  
Michael I. Ganzburg
Keyword(s):  
Sharp Constants ◽  
Exponential Weights

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model

2020 ◽  
Vol 8 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Coarse Graining ◽  
Exponential Weights ◽  
Percolation Process ◽  
Last Passage Percolation ◽  
Corner Growth Model ◽  
And Control

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

General sharp weighted Caffarelli–Kohn–Nirenberg inequalities

2018 ◽  
Vol 149 (03) ◽  
pp. 691-718 ◽  
Author(s):  
Nguyen Lam
Keyword(s):  
Mass Transport ◽  
Sharp Constants ◽  
Optimal Mass Transport

AbstractIn this paper, we will use optimal mass transport combining with suitable transforms to study the sharp constants and optimizers for a class of the Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities. Moreover, we will investigate these inequalities with and without the monomial weights $x_{1}^{A_{1}} \cdots x_{N}^{A_{N}}$ on ℝN.

SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE

2004 ◽  
Vol 06 (05) ◽  
pp. 781-792 ◽  
Author(s):  
MEIJUN ZHU
Keyword(s):  
Riemannian Manifold ◽  
Sobolev Inequalities ◽  
Square Root ◽  
Two Dimensional ◽  
Closed Geodesics ◽  
Sharp Constants ◽  
Simple Closed Geodesics

We show that the sharp constants of Poincaré–Sobolev inequalities for any smooth two dimensional Riemannian manifold are less than or equal to [Formula: see text]. For a smooth topological two sphere M2, the sharp constants are [Formula: see text] if and only if M2 is isometric to two sphere S2 with the standard metric. In the same spirit, we show that for certain special smooth topological sphere the ratio between the shortest length of simple closed geodesics and the square root of its area is less than or equals to [Formula: see text].

scholarly journals Bellman function approach to the sharp constants in uniform convexity

2018 ◽  
Vol 11 (1) ◽  
pp. 89-93
Author(s):  
Paata Ivanisvili
Keyword(s):  
Uniform Convexity ◽  
Function Approach ◽  
Function Technique ◽  
Bellman Function ◽  
Sharp Constants

AbstractWe illustrate a Bellman function technique in finding the modulus of uniform convexity of {L^{p}} spaces.

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