Heat kernels on metric spaces and a characterisation of constant functions

2004 ◽  
Vol 115 (3) ◽  
pp. 389-399 ◽  
Author(s):  
Katarzyna Pietruska-Pałuba
Keyword(s):  
Metric Spaces ◽  
Heat Kernels

scholarly journals Diffusion processes and heat kernels on metric spaces

1998 ◽  
Vol 26 (1) ◽  
pp. 1-55 ◽  
Author(s):  
K. T. Sturm
Keyword(s):  
Metric Spaces ◽  
Diffusion Processes ◽  
Heat Kernels

scholarly journals Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces

2016 ◽  
Vol 45 (4) ◽  
pp. 609-633 ◽  
Author(s):  
Niko Marola ◽  
Michele Miranda ◽  
Nageswari Shanmugalingam
Keyword(s):  
Metric Spaces ◽  
Heat Kernels ◽  
Sets Of Finite Perimeter ◽  
Finite Perimeter

scholarly journals AN ANALYTICAL APPROACH TO HEAT KERNEL ESTIMATES ON STRONGLY RECURRENT METRIC SPACES

2008 ◽  
Vol 51 (1) ◽  
pp. 171-199 ◽  
Author(s):  
Jiaxin Hu
Keyword(s):  
Dirichlet Boundary ◽  
Metric Spaces ◽  
Dirichlet Forms ◽  
Upper Bounds ◽  
Heat Kernels ◽  
Dirichlet Boundary Conditions ◽  
Green Functions ◽  
Compact Embedding ◽  
Kernel Estimates ◽  
Compact Metric Spaces

AbstractIn this paper we prove that sub-Gaussian estimates of heat kernels of regular Dirichlet forms are equivalent to the regularity of measures, two-sided bounds of effective resistances and the locality of semigroups, on strongly recurrent compact metric spaces. Upper bounds of effective resistances imply the compact embedding theorem for domains of Dirichlet forms, and give rise to the existence of Green functions with zero Dirichlet boundary conditions. Green functions play an important role in our analysis. Our emphasis in this paper is on the analytic aspects of deriving two-sided sub-Gaussian bounds of heat kernels. We also give the probabilistic interpretation for each of the main analytic steps.

Heat Kernels on Metric Spaces with Doubling Measure

2009 ◽  
pp. 3-44 ◽  
Author(s):  
Alexander Grigor’yan ◽  
Jiaxin Hu ◽  
Ka-Sing Lau
Keyword(s):  
Metric Spaces ◽  
Heat Kernels ◽  
Doubling Measure

Crystallography in two-dimensional metric spaces*

1969 ◽  
Vol 130 (1-6) ◽  
pp. 277-303 ◽  
Author(s):  
Aloysio Janner ◽  
Edgar Ascher
Keyword(s):  
Metric Spaces ◽  
Two Dimensional

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

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