Download E-books Isometric Embedding of Riemannian Manifolds in Euclidean Spaces (Mathematical Surveys and Monographs) PDF

The query of the life of isometric embeddings of Riemannian manifolds in Euclidean house is already greater than a century outdated. This ebook offers, in a scientific means, effects either neighborhood and worldwide and in arbitrary size yet with a spotlight at the isometric embedding of surfaces in ${\mathbb R}^3$. The emphasis is on these PDE thoughts that are necessary to an important result of the final century. The vintage leads to this ebook contain the Janet-Cartan Theorem, Nirenberg's answer of the Weyl challenge, and Nash's Embedding Theorem, with a simplified evidence via Günther. The booklet additionally contains the most effects from the earlier 20 years, either neighborhood and worldwide, at the isometric embedding of surfaces in Euclidean 3-space. The paintings may be necessary to researchers within the quarter. in addition, the authors combine the consequences and methods right into a unified entire, supplying an exceptional access element into the realm for complex graduate scholars or a person attracted to this topic. The authors stay away from what's technically advanced. history wisdom is stored to a vital minimal: a one-semester path in differential geometry and a one-year path in partial differential equations.

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