Super-Ricci flows and improved gradient and transport estimates

• 成果类型: Article
• 署名作者: Kopfer, Eva
• 署名单位: University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00904-6
• 发表日期: 2019
• 页码: 897-936
• 关键词: metric-measure-spaces; curvature-dimension condition; EQUIVALENCE; entropy

摘要

We introduce Brownian motions on time-dependent metric measure spaces, proving their existence and uniqueness. We prove contraction estimates for their trajectories assuming that the time-dependent heat flow satisfies transport estimates with respect to every L-p-Kantorovich distance, p. [1,8]. These transport estimates turn out to characterize super-Ricci flows, introduced by Sturm (J Funct Anal 275(12):3504-3569, 2015.)