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

^*Corresponding author

International School for Advanced Studies

Research output: Contribution to journal › Article

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.

Original language	English
Pages (from-to)	377-386
Number of pages	10
Journal	ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume	29
DOIs	https://doi.org/10.4171/RLM/811
Publication status	Published - 2018

Keywords

Optimal transport
RCD spaces
Schrodinger problem
entropic interpolation
metric geometry

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title = "Mathematical Analysis {\textemdash} Second order differentiation formula on RCD(K,N) spaces",

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",

year = "2018",

doi = "10.4171/RLM/811",

language = "English",

volume = "29",

pages = "377--386",

journal = "ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI",

issn = "1120-6330",

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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TY - JOUR

T1 - Mathematical Analysis — Second order differentiation formula on RCD(K,N) spaces

AU - Gigli, Nicola

AU - Tamanini, Luca

PY - 2018

Y1 - 2018

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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