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Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds

Fengyu Wang, Bo Wu, Feng-yu Wang Orcid Logo

Science China Mathematics, Volume: 61, Issue: 8, Pages: 1407 - 1420

Swansea University Author: Feng-yu Wang Orcid Logo

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DOI (Published version): 10.1007/s11425-017-9296-8

Abstract

Let $M$ be a complete Riemannian manifold possibly with a boundary $\pp M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=\DD+Z$, pointwise characterizations are presented for the Bakry-Emery curvature of $L$ and the...

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Published in: Science China Mathematics
ISSN: 1674-7283 1869-1862
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URI: https://cronfa.swan.ac.uk/Record/cronfa43218
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first_indexed 2018-08-04T03:57:49Z
last_indexed 2019-03-26T12:14:39Z
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spelling 2019-03-25T12:27:04.5293972 v2 43218 2018-08-04 Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds 6734caa6d9a388bd3bd8eb0a1131d0de 0000-0003-0950-1672 Feng-yu Wang Feng-yu Wang true false 2018-08-04 SMA Let $M$ be a complete Riemannian manifold possibly with a boundary $\pp M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=\DD+Z$, pointwise characterizations are presented for the Bakry-Emery curvature of $L$ and the second fundamental form of $\pp M$ if exists. These extend and strengthen the recent results derived by A. Naber for the uniform norm $\|\Ric_Z\|_\infty$ on manifolds without boundary. A key point of the present study is to apply the asymptotic formulas for these two tensors found by the first named author, such that the proofs are significantly simplified. Journal Article Science China Mathematics 61 8 1407 1420 1674-7283 1869-1862 0 0 0 0001-01-01 10.1007/s11425-017-9296-8 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-03-25T12:27:04.5293972 2018-08-04T01:33:25.8839048 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Fengyu Wang 1 Bo Wu 2 Feng-yu Wang 0000-0003-0950-1672 3 0043218-04082018013737.pdf 18SCI.pdf 2018-08-04T01:37:37.3730000 Output 214727 application/pdf Corrected Version of Record true 2019-05-14T00:00:00.0000000 true eng
title Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
spellingShingle Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
Feng-yu Wang
title_short Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
title_full Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
title_fullStr Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
title_full_unstemmed Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
title_sort Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Fengyu Wang
Bo Wu
Feng-yu Wang
format Journal article
container_title Science China Mathematics
container_volume 61
container_issue 8
container_start_page 1407
institution Swansea University
issn 1674-7283
1869-1862
doi_str_mv 10.1007/s11425-017-9296-8
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description Let $M$ be a complete Riemannian manifold possibly with a boundary $\pp M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=\DD+Z$, pointwise characterizations are presented for the Bakry-Emery curvature of $L$ and the second fundamental form of $\pp M$ if exists. These extend and strengthen the recent results derived by A. Naber for the uniform norm $\|\Ric_Z\|_\infty$ on manifolds without boundary. A key point of the present study is to apply the asymptotic formulas for these two tensors found by the first named author, such that the proofs are significantly simplified.
published_date 0001-01-01T03:54:29Z
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score 11.035634

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