On the local isometric embedding in (3) of surfaces with zero sets of Gaussian curvature forming cusp domains

Lin Tsung-Yin

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On the local isometric embedding in (3) of surfaces with zero sets of Gaussian curvature forming cusp domains

机译：关于（3）具有零组高斯曲率形成尖端区域的表面的局部等距嵌入

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摘要

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 suciently smooth isometric embeddings exist.

机译：我们研究了将二维黎曼流形等轴测地嵌入到欧几里得三空间中的问题。结果表明，如果高斯曲率消失为有限阶并且其零集由在点处相切的两条平滑曲线组成，则存在局部充分光滑的等距嵌入。

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来源
《Communications in Partial Differential Equations》 |2016年第12期|共40页
作者
Lin Tsung-Yin;
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原文格式 PDF
正文语种 eng
中图分类偏微分方程;
关键词
Cusp domain; local isometric embedding; Monge-Ampere equation;

机译：尖点域;局部等距嵌入;Monge-Ampere方程;

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专利

1. On the local isometric embedding in (3) of surfaces with zero sets of Gaussian curvature forming cusp domains [J] . Lin Tsung-Yin Communications in Partial Differential Equations . 2016,第10a12期

机译：关于（3）具有零组高斯曲率形成尖端区域的表面的局部等距嵌入
2. Local isometric embedding of surfaces with nonpositive Gaussian curvature [J] . Qing Han, Jia-Xing Hong, Chang-Shou Lin Journal of Differential Geometry . 2003,第3期

机译：具有非正高斯曲率的曲面的局部等距嵌入
3. THE LOCAL ISOMETRIC EMBEDDING IN R~3 OF TWO-DIMENSIONAL RIEMANNIAN MANIFOLDS WITH GAUSSIAN CURVATURE CHANGING SIGN TO FINITE ORDER ON A CURVE [J] . Marcus A. Khuri Journal of Differential Geometry . 2007,第2期

机译：具有二维高斯曲线变化符号的二维黎曼流形在R〜3中的局部等价嵌入
4. Self-folding Origami Surfaces of Non-Zero Gaussian Curvature [C] . Milton R. Garza, Edwin A. Peraza Hernandez, Darren J. Hartl Behavior and Mechanics of Multifunctional Materials XIII . 2019

机译：非零高斯曲率的自折叠折纸表面
5. The local isometric embedding in R3 of two-dimensional Riemannian manifolds with Gaussian curvature changing sign to finite order on a curve. [D] . Khuri, Marcus A. 2003

机译：二维黎曼流形在R3中的局部等距嵌入，其中高斯曲率的符号在曲线上变为有限阶。
6. Geodesic curvature driven surface microdomain formation [O] . Melissa R. Adkins, Y. C. Zhou -1

机译：测地曲率驱动的表面微区形成
7. On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign [O] . Han, Qing, Khuri, Marcus 2010

机译：用高斯分布在R ^ 3曲面上局部等距嵌入混合标志的曲率

On the local isometric embedding in (3) of surfaces with zero sets of Gaussian curvature forming cusp domains

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