On the Local Isometric Embedding in R³ of Surfaces with Zero Sets of Gaussian Curvature Forming Cusp Domains

2015/10/26 by Tsung-Yin Lin, Lin, Tsung-Yin
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1510.07505

arXiv admin note: text overlap with arXiv:1009.6214 by other authors

arxiv created 2015/10/26 · openalex publication_date 2015/10/26 · arxiv updated 2015/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a point, then local sufficiently smooth isometric embedding exists.

Citations

• On the Local Isometric Embedding in R³ of Surfaces with Gaussian Curvature of Mixed Sign

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