Abstract
In this paper, we obtain some rigidity theorems for compact Riemannian manifolds Ω with boundary M and nonnegative Ricci curvature; for instance, we prove that the existence of certain functions on M together with a lower bound c > 0 on the principal curvtures of M imply that Ω is an euclidean ball of radius \( {1\over c} \).
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To S.S. Chern on his 90th birthday
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do Carmo, M., Xia, C. Rigidity Theorems for Manifolds with Boundary and Nonnegative Ricci Curvature. Results. Math. 40, 122–129 (2001). https://doi.org/10.1007/BF03322702
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DOI: https://doi.org/10.1007/BF03322702