Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

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

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Additional Info

Field	Value
Source	https://hal.science/hal-00769378
Author	Ambrosio, Luigi, Gigli, Nicola, Savaré, Giuseppe
Maintainer	CCSD
Last Updated	May 29, 2026, 04:12 (UTC)
Created	May 29, 2026, 04:12 (UTC)
Identifier	hal-00769378
Language	en
contributor	Scuola Normale Superiore di Pisa (SNS)
creator	Ambrosio, Luigi
date	2012-09-07T00:00:00
harvest_object_id	537a05d3-dbba-483a-8aca-a3138114a0f2
harvest_source_id	3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title	test moissonnage SELUNE
metadata_modified	2025-06-23T00:00:00
relation	info:eu-repo/semantics/altIdentifier/arxiv/1106.2090
set_spec	type:UNDEFINED