Mathematical Analysis — Second order differentiation formula on RCD(K,N) spaces

Nicola Gigli; Luca Tamanini

doi:10.4171/RLM/811

Mathematical Analysis — Second order differentiation formula on RCD(K,N) spaces

Nicola Gigli^*, Luca Tamanini

^*Autore corrispondente per questo lavoro

International School for Advanced Studies

Risultato della ricerca: Contributo in rivista › Articolo in rivista

Abstract

We prove the second order differentiation formula along geodesics in finite-dimensional RCD(K, N) spaces. Our approach strongly relies on the approximation of W-2-geodesics by entropic interpolations and, in order to implement this approximation procedure, on the proof of new (even in the smooth setting) estimates for such interpolations.

Lingua originale	English
pagine (da-a)	377-386
Numero di pagine	10
Rivista	ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume	29
DOI	https://doi.org/10.4171/RLM/811
Stato di pubblicazione	Pubblicato - 2018

Keywords

Optimal transport
RCD spaces
Schrodinger problem
entropic interpolation
metric geometry

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abstract = "We prove the second order differentiation formula along geodesics in finite-dimensional RCD(K, N) spaces. Our approach strongly relies on the approximation of W-2-geodesics by entropic interpolations and, in order to implement this approximation procedure, on the proof of new (even in the smooth setting) estimates for such interpolations.",

keywords = "Optimal transport, RCD spaces, Schrodinger problem, entropic interpolation, metric geometry, Optimal transport, RCD spaces, Schrodinger problem, entropic interpolation, metric geometry",

author = "Nicola Gigli and Luca Tamanini",

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doi = "10.4171/RLM/811",

language = "English",

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publisher = "Accademia Nazionale dei Lincei:Via Lungara 10 Uff Diff Pubbl., I 00165 Rome Italy:011 39 06 68027230, EMAIL: [email protected], INTERNET: http://www.lincei.it, Fax: 011 39 06 68027334",

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AU - Gigli, Nicola

AU - Tamanini, Luca

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N2 - We prove the second order differentiation formula along geodesics in finite-dimensional RCD(K, N) spaces. Our approach strongly relies on the approximation of W-2-geodesics by entropic interpolations and, in order to implement this approximation procedure, on the proof of new (even in the smooth setting) estimates for such interpolations.

AB - We prove the second order differentiation formula along geodesics in finite-dimensional RCD(K, N) spaces. Our approach strongly relies on the approximation of W-2-geodesics by entropic interpolations and, in order to implement this approximation procedure, on the proof of new (even in the smooth setting) estimates for such interpolations.

KW - Optimal transport

KW - RCD spaces

KW - Schrodinger problem

KW - entropic interpolation

KW - metric geometry

KW - Optimal transport

KW - RCD spaces

KW - Schrodinger problem

KW - entropic interpolation

KW - metric geometry

UR - http://hdl.handle.net/10807/232498

U2 - 10.4171/RLM/811

DO - 10.4171/RLM/811

M3 - Article

SN - 1120-6330

VL - 29

SP - 377

EP - 386

JO - ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI

JF - ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI

ER -

Mathematical Analysis — Second order differentiation formula on RCD(K,N) spaces

Abstract

Keywords

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