Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-19T23:08:23.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean Curvature Comparison with ${{L}^{1}}$-norms of Ricci Curvature

Published online by Cambridge University Press:  20 November 2018

Jong-Gug Yun
Jong-Gug Yun*
Affiliation:
Department of Mathematic Sciences Seoul National University Seoul 151-747 Korea, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove an analogue of mean curvature comparison theorem in the case where the Ricci curvature below a positive constant is small in ${{L}^{1}}$-norm.

Keywords

53C20mean curvatureRicci curvature
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 314 - 320
Copyright
Copyright © Canadian Mathematical Society 2004

References

[CK] Croke, C. and Karcher, H., Volumes of small balls on open manifolds: lower bounds and examples. Trans. Amer.Math. Soc. 309 (1988), 753–762.Google Scholar
[G] Gallot, S., Isoperimetric inequalities based on integral norms of Ricci curvature. Ast érisque 18 (1983), 191–216.Google Scholar
[P] Paeng, S.-H., A sphere theorem under a curvature perturbation II. Kyushu J. Math. 52(1998) 439–454.Google Scholar
[PS] Petersen, P. and Sprouse, C., Integral curvature bounds, distance estimates and applications. J. Differential Geom. 50 (1998), 269–298.Google Scholar
[S] Sprouse, C., Integral curvature bounds and bounded diamter. Comm. Anal. Geom. 8 (2000), 531–543.Google Scholar