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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hengrong Du ◽  
Qinfeng Li ◽  
Changyou Wang

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.


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

Author(s):  
YAXIANG LI ◽  
SAMINATHAN PONNUSAMY ◽  
QINGSHAN ZHOU

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.


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

Sign in / Sign up

Export Citation Format

Share Document