Journal article 863 views 171 downloads
Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds
Fengyu Wang,
Bo Wu,
Feng-yu Wang 
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 |
| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa43218 |
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| 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 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
8 |
| Start Page: |
1407 |
| End Page: |
1420 |