Isometric embedding of Riemannian manifolds into Euclidean spaces
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Speaker: Wentao Cao (University of Leipzig)
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Time: Jun 16, 2020, 16:30-17:30
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Location: Zoom (ID 69481214342)
Isometric embedding of Riemannian manifolds into Euclidean space is a classical problem in differential geometry. In this talk, after introducing some literature on such topic, I will present my recent works on isometric embeddings of different regularity. First I will show global C^{1, \theta} Nash-Kuiper theorems for compact manifolds with sharper Holder exponent, which is about the flexibility of isometric embedding, through the powerful technique of convex integration. Then I will also show my Ph. D works on C^{1, 1} isometric immersions of two types of metric by compensated compactness theory and global smooth isometric immersions of negatively curved surfaces with slowly decaying curvature through the characteristic method.
