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Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
Science China Mathematics, Volume: 61, Issue: 8, Pages: 1407 - 1420
Swansea University Author:
Feng-yu Wang
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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...
Published in: | Science China Mathematics |
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ISSN: | 1674-7283 1869-1862 |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa43218 |
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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 |
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61 |
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8 |
container_start_page |
1407 |
institution |
Swansea University |
issn |
1674-7283 1869-1862 |
doi_str_mv |
10.1007/s11425-017-9296-8 |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
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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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1763752719652225024 |
score |
11.021648 |