Isometric embedding with nonnegative Gauss curvature under the graph setting

2018/06/16 by Xumin Jiang, Jiang, Xumin
Mathematics · Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders

paper · pdf · doi:10.48550/arxiv.1806.06189

Abstract

We study the regularity of the isometric embedding X: (B(O,r),g) -> (R3, gcan) of a 2-ball with nonnegatively curved C4 metric into R3. Under the assumption that X can be expressed in the graph form, we show X is C2,1 near P, which is optimal by Iaia's example.

Related

• Counterexamples for Local Isometric Embedding
• On the mean curvature of Nash isometric embeddings
• A free boundary isometric embedding problem in the unit ball
• On the Local Isometric Embedding in R³ of Surfaces with Zero Sets of Gaussian Curvature Forming Cusp Domains
• The Weyl problem with nonnegative Gauss curvature in hyperbolic space