文摘
英文文摘
Chapter 1 Optimal Transportation and Curvature-Dimension Condition
1.1 L2 Wasserstein Spaces
1.2 Prékopa-Leindler inequality and Brunn Minkowski inequality
1.3 Shannon Entropy and Rényi Entropy on The Space of Probability Measures
1.3.1 Shannon Entropy
1.3.2 Rényi Entropy
1.4 The Convexity of Entropies and the Curvature-Dimension Condition for Metric Measure Spaces
1.5 Tensorization Property of The Curvature-Dimension Condition
1.6 Disproving Conjecture 30.34 in[38]
Chapter 2 Complete Hypersurfaces with Constant Mean Curvature and Finite Index in Hyperbolic Spaces
2.1 Introduction
2.2 Proofs of The Theorems
Chapter 3 Constant Mean Curvature Hypersurfaces in Spheres
3.1 Introduction
3.1.1 Minimal hypersurfaces in Sn+1
3.1.2 Constant mean curvature hypersurfaces in Sn+1
3.2 Basic Formulas for Closed Hypersurfaces with Constant Mean Curvature H in Sn+1(1)
3.3 Proofs of The Theorem
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