HAL (Le Centre pour la Communication Scientifique Directe)· 2012· Preprint
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
- 373citations
- 2012year
Short summary
A revised framework for calculus and heat flow in metric measure spaces with Ricci bounds from below is presented, featuring simplified proofs and new/augmented results.
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Key points
- Introduces a revised framework for calculus and heat flow in metric measure spaces with Ricci bounds from below.
- Includes new lemmas (2.4, 2.10), propositions (5.7, 4.8, 4.15), and theorems (6.3, 4.16).
- Augments and reinforces existing results (4.7, 4.8, 4.15, 4.16).
- Simplifies proofs for Theorem 4.16 and Lemma 9.6.
- Proposes a simpler, equivalent axiomatization for weak gradients.
AI-generated from the title and abstract; the full text is not read.
Abstract
Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been proposed
The authors' abstract, as published at the source. HAL (Le Centre pour la Communication Scientifique Directe), 2012 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics