Curvature integral estimates for complete hypersurfaces

2009/03/11 by Hilário Alencar, Alencar, Hilário, Walcy Santos +3 · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0903.2035

Abstract

We consider the integrals of r-mean curvatures S_r of a complete hypersurface M in space forms Q_cⁿ⁺¹ which generalize volume (r=0), total mean curvature (r=1), total scalar curvature (r=2) and total curvature (r=n). Among other results we prove that a complete properly immersed hypersurface of a space form with S_r≥ 0, S_r\not≡ 0 and S_r+1≡ 0 for some r≤ n-1 has ∫_MS_rdM=∞.

Cited by

• Stable hypersurfaces with constant scalar curvature in Euclidean spaces
• Caccioppoli's inequalities on constant mean curvature hypersurfaces in\n Riemannian manifolds

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