Boundary estimates for the Ricci flow

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• 作者：Panagiotis Gianniotis
• 关键词：Primary ; 53C44 ; Secondary ; 35K51
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：55
• 期：1
• 全文大小：539 KB
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  16.Pulemotov, A.: Quasilinear parabolic equations and the Ricci flow on manifolds with boundary. J. Reine Angew. Math. 683, 97–118 (2013)MathSciNet
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• 作者单位：Panagiotis Gianniotis (1)
  
  1. Department of Mathematics, University College London, 25 Gordon St, London, WC1E 6BT, UK
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

In this paper we consider the Ricci flow on manifolds with boundary with appropriate control on its mean curvature and conformal class. We obtain higher order estimates for the curvature and second fundamental form near the boundary, similar to Shi’s local derivative estimates. As an application, we prove a version of Hamilton’s compactness theorem in which the limit has boundary. Finally, we show that in dimension three the second fundamental form of the boundary and its derivatives are a priori controlled in terms of the ambient curvature and some non-collapsing assumptions. In particular, the flow exists as long as the curvature remains bounded, in contrast to the general case where control on the second fundamental form is also required. Mathematics Subject Classification Primary: 53C44 Secondary: 35K51