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Global Analysis of Minimal Surfaces

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556 pages

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The exploration of minimal surfaces is deepened through a focus on existence, regularity, and uniqueness theorems for surfaces with partially free boundaries, highlighting the concept of "edge-crawling." A priori estimates for higher-dimensional minimal surfaces and singular integral minimizers are also discussed, leading to significant Bernstein theorems. Additionally, the book presents a comprehensive global theory, addressing the Douglas problem with Teichmüller theory, deriving index theorems, and introducing a topological perspective through Fredholm vector fields, all reflecting Smale's vision.

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ISBN
9783642117053

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Book variant

2010, hardcover

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