Boundary effect of m-dimensional Bakry-Émery Ricci curvature

Boundary effect of m-dimensional Bakry-Émery Ricci curvature Anal.Math.Phys. https://doi.org/10.1007/s13324-018-0237-5 Boundary effect of m-dimensional Bakry-Émery Ricci curvature 1 2 Qiang Tu · Guangyue Huang Received: 23 June 2017 / Revised: 24 March 2018 / Accepted: 27 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract We consider how m-dimensional Bakry-Émery Ricci curvature affects the geometry of the boundary ∂ M. By using the Reilly’s formula with respect to f -Laplacian, geometric inequalities involving f -mean curvature are obtained. Fur- thermore, we also achieve the relationship between f -mean curvature of the boundary submanifold and the mean curvature of submanifold x : ∂ M → R (c) into space form R (c). Keywords f -mean curvature · Boundary effect · m-dimensional Bakry-Émery Ricci curvature Mathematics Subject Classification Primary 53C42; Secondary 53C21 1 Introduction Let (M, g) be an n-dimensional compact Riemannian manifold with nonempty smooth boundary ∂ M.In[10], Miao and Wang consider the question how the Ricci curva- The research of authors is supported by Hubei Key Laboratory of Applied Mathematics (Hubei University) and NSFC(No. 11371018, 11671121). B Qiang Tu qiangtu@whu.edu.cn Guangyue Huang hgy@henannu.edu.cn Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, People’s Republic of China Department of Mathematics, Henan Normal University, Xinxiang http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Boundary effect of m-dimensional Bakry-Émery Ricci curvature

Loading next page...
 
/lp/springer_journal/boundary-effect-of-m-dimensional-bakry-mery-ricci-curvature-N1676AMmAM
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
D.O.I.
10.1007/s13324-018-0237-5
Publisher site
See Article on Publisher Site

Abstract

Anal.Math.Phys. https://doi.org/10.1007/s13324-018-0237-5 Boundary effect of m-dimensional Bakry-Émery Ricci curvature 1 2 Qiang Tu · Guangyue Huang Received: 23 June 2017 / Revised: 24 March 2018 / Accepted: 27 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract We consider how m-dimensional Bakry-Émery Ricci curvature affects the geometry of the boundary ∂ M. By using the Reilly’s formula with respect to f -Laplacian, geometric inequalities involving f -mean curvature are obtained. Fur- thermore, we also achieve the relationship between f -mean curvature of the boundary submanifold and the mean curvature of submanifold x : ∂ M → R (c) into space form R (c). Keywords f -mean curvature · Boundary effect · m-dimensional Bakry-Émery Ricci curvature Mathematics Subject Classification Primary 53C42; Secondary 53C21 1 Introduction Let (M, g) be an n-dimensional compact Riemannian manifold with nonempty smooth boundary ∂ M.In[10], Miao and Wang consider the question how the Ricci curva- The research of authors is supported by Hubei Key Laboratory of Applied Mathematics (Hubei University) and NSFC(No. 11371018, 11671121). B Qiang Tu qiangtu@whu.edu.cn Guangyue Huang hgy@henannu.edu.cn Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, People’s Republic of China Department of Mathematics, Henan Normal University, Xinxiang

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: May 30, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off