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In this work we establish a sharp geometric inequality for closedhypersurfaces in complete noncompact Riemannian manifolds with asymptoticallynonnegative curvature using standard comparison methods in Riemannian Geometry.These methods have been applied in a recent work by Xiaodong Wang to greatlysimplify the proof of a Willmore-type inequality in complete noncompactRiemannian manifolds of nonnegative Ricci curvature, which was first proved byAgostiniani, Fagagnolo and Mazzieri.

A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature