Type
Text
Type
Dissertation
Advisor
Sun, Song | Khuri, Marcus A. | Rachev, Svetlozar. | Chen, Xiuxiong
Date
2015-12-01
Keywords
Mathematics | cusp, geometric analysis, isometric embedding, Nash-Moser iteration, partial differential equations
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76402
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a point, then local sufficiently smooth isometric embeddings exist. | 64 pages
Recommended Citation
Lin, Tsung-Yin, "On the local isometric embedding in R^3 of surfaces with zero sets of Gaussian curvature forming cusp domains" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2325.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2325