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A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature
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In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompact Riemannian manifolds with asymptotically nonnegative curvature using standard comparison methods in Riemannian Geometry. These methods have been applied in a recent work by Xiaodong Wang to greatly simplify the proof of a Willmore-type inequality in complete noncompact Riemannian manifolds of nonnegative Ricci curvature, which was first proved by Agostiniani, Fagagnolo and Mazzieri.
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Cited by 2 Pith papers
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Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature
The paper proves a Fenchel-Willmore-Chen inequality for submanifolds in smooth metric measure spaces with lower bounds on the 1-Bakry-Emery n-Ricci curvature, plus Sobolev and isoperimetric inequalities under nonnegat...
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A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds
For bounded domains in complete non-compact manifolds, Willmore-type inequalities hold under asymptotic or Lp Ricci curvature bounds, recovering the pointwise Jin-Yin theorem as a limit.
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