A rigidity result for metric measure spaces with Euclidean heat kernel Article Swipe

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YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.5802/jep.179

We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding’s celebrated almost rigidity volume theorem via a quantitative version of our main result. We also discuss the case of a metric measure space equipped with a Dirichlet form admitting a spherical heat kernel.

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Mathematics

Euclidean Geometry

Performance Indicator

Metric Space

Mathematical Analysis

Dirichlet Distribution

Operations Management

Quantum Mechanics

Database

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Heat kernel Mathematics Measure (data warehouse) Dirichlet form Euclidean space Euclidean distance Rigidity (electromagnetism) Euclidean geometry Metric (unit) Metric space Seven-dimensional space Intrinsic metric Pure mathematics Mathematical analysis Dirichlet distribution Convex metric space Euclidean distance matrix Computer science Physics Geometry Economics Operations management Quantum mechanics Boundary value problem Database

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Type: article
Language: en
Landing Page: https://doi.org/10.5802/jep.179
PDF: https://jep.centre-mersenne.org/item/10.5802/jep.179.pdf
OA Status: diamond
Cited By: 5
References: 43
Related Works: 10
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DOI: https://doi.org/10.5802/jep.179

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Title: A rigidity result for metric measure spaces with Euclidean heat kernel

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Language: en

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Publication year: 2021

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Publication date: 2021-11-17

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Authors: Gilles Carron, David Tewodrose

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Landing page: https://doi.org/10.5802/jep.179

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Concepts: Heat kernel, Mathematics, Measure (data warehouse), Dirichlet form, Euclidean space, Euclidean distance, Rigidity (electromagnetism), Euclidean geometry, Metric (unit), Metric space, Seven-dimensional space, Intrinsic metric, Pure mathematics, Mathematical analysis, Dirichlet distribution, Convex metric space, Euclidean distance matrix, Computer science, Physics, Geometry, Economics, Operations management, Quantum mechanics, Boundary value problem, Database

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Cited by: 5

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