The Apollonian inner metric and uniform domains

2010 ◽  
Vol 283 (9) ◽  
pp. 1277-1290 ◽  
Author(s):  
M. Huang ◽  
S. Ponnusamy ◽  
X. Wang ◽  
S. K. Sahoo
Keyword(s):  
Uniform Domains ◽  
Inner Metric

scholarly journals INNER UNIFORM DOMAINS AND THE APOLLONIAN INNER METRIC

2013 ◽  
Vol 50 (6) ◽  
pp. 1873-1886
Author(s):  
Yaxiang Li ◽  
Xiantao Wang
Keyword(s):  
Uniform Domains ◽  
Inner Metric

Compactness of 𝑀-uniform domains and optimal thermal insulation problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hengrong Du ◽  
Qinfeng Li ◽  
Changyou Wang
Keyword(s):  
Thermal Insulation ◽  
Heat Insulation ◽  
Optimization Problems ◽  
Optimal Shape ◽  
Optimal Heat ◽  
Optimal Shapes ◽  
Stable Solutions ◽  
Uniform Domains

Abstract In this paper, we will consider an optimal shape problem of heat insulation introduced by [D. Bucur, G. Buttazzo and C. Nitsch, Two optimization problems in thermal insulation, Notices Amer. Math. Soc. 64 (2017), 8, 830–835]. We will establish the existence of optimal shapes in the class of 𝑀-uniform domains. We will also show that balls are stable solutions of the optimal heat insulation problem.

scholarly journals On Removability Properties of $$\psi $$ ψ -Uniform Domains in Banach Spaces

2016 ◽  
Vol 11 (1) ◽  
pp. 35-55
Author(s):  
M. Huang ◽  
M. Vuorinen ◽  
X. Wang
Keyword(s):  
Banach Spaces ◽  
Uniform Domains

SPHERICALIZATION AND FLATTENING PRESERVE UNIFORM DOMAINS IN NONLOCALLY COMPACT METRIC SPACES

2020 ◽  
pp. 1-22
Author(s):  
YAXIANG LI ◽  
SAMINATHAN PONNUSAMY ◽  
QINGSHAN ZHOU
Keyword(s):  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Spaces ◽  
Möbius Maps ◽  
Compact Metric Spaces ◽  
Uniform Domains ◽  
Invariant Properties

The main aim of this paper is to investigate the invariant properties of uniform domains under flattening and sphericalization in nonlocally compact complete metric spaces. Moreover, we show that quasi-Möbius maps preserve uniform domains in nonlocally compact spaces as well.

A note on ϕ-uniform domains

2016 ◽  
Vol 24 (1) ◽  
pp. 51-56
Author(s):  
Debanjan Nandi
Keyword(s):  
Uniform Domains
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