Finiteness of Index and Total Scalar Curvature for Minimal Hypersurfaces

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Minimal hypersurfaces in H × R, total curvature and index

In this paper, we consider minimal hypersurfaces in the product space Hn × R. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total int...

متن کامل

Positive Scalar Curvature and Minimal Hypersurfaces

We show that the minimal hypersurface method of Schoen and Yau can be used for the “quantitative” study of positive scalar curvature. More precisely, we show that if a manifold admits a metric g with sg ≥ |T | or sg ≥ |W |, where sg is the scalar curvature of of g, T any 2-tensor on M and W the Weyl tensor of g, then any closed orientable stable minimal (totally geodesic in the second case) hyp...

متن کامل

06 Singular Minimal Hypersurfaces and Scalar Curvature

Finding obstructions to positive scalar curvature and getting structural insight is presently based on two competing approaches: one path which is most travelled works in the context of spin geometry and gives quite a direct link to topology (cf. [GL1-2] and [G]). The second, much less used but a priori more general method of attack analyzes minimal hypersurfaces within the manifold under consi...

متن کامل

On the Average of the Scalar Curvature of Minimal Hypersurfaces of Spheres with Low Stability Index

In this paper we show that if the stability index of M is equal to n+2, then the average of the function |A|2 is less than or equal to n − 1. Moreover, if this average is equal to n − 1, then M must be isometric to a Clifford minimal hypersurface.

متن کامل

A ug 2 00 8 Minimal hypersurfaces in H n × R , total curvature and index

In this paper, we consider minimal hypersurfaces in the product space Hn×R. We study the relation between the notions of finite total curvature and index of the stability operator. We study examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations; they serve as counterexamples and are useful barriers for many geometric problems.1

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1989

ISSN: 0002-9939

DOI: 10.2307/2046961