A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport

We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non-smooth metric measure spaces with Ricci curvature bounded from below.

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Field	Value
Source	https://hal.science/hal-00769367
Author	Gigli, Nicola, Mantegazza, Carlo
Maintainer	CCSD
Last Updated	May 29, 2026, 03:50 (UTC)
Created	May 29, 2026, 03:50 (UTC)
Identifier	hal-00769367
Language	en
contributor	Laboratoire Jean Alexandre Dieudonné (LJAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)
creator	Gigli, Nicola
date	2012-08-28T00:00:00
harvest_object_id	3651b39e-2727-4dcd-b6c8-6fad38c71fda
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/1208.5815
set_spec	type:UNDEFINED