اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRemark on an inequality for closed hypersurfaces in complete manifolds with nonnegative Ricci curvature
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Xiaodong Wang
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We give a simple proof of a recent result due to Agostiniani, Fogagnolo and Mazzieri.
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In this paper we provide some local and global splitting results on complete Riemannian manifolds with nonnegative Ricci curvature. We achieve the splitting through the analysis of some pointwise inequalities of Modica type which hold true for every
bounded solution to a semilinear Poisson equation. More precisely, we prove that the existence of a nonconstant bounded solution $u$ for which one of the previous inequalities becomes an equality at some point leads to the splitting results as well as to a classification of such a solution $u$.
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Let M be a Riemannian n-manifold with n greater than or equal to 3. For k between 1 and n, we say M has k-positive Ricci curvature if at every point of M the sum of any k eigenvalues of the Ricci curvature is strictly positive. In particular, one pos
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