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Minimal Legendrian Surfaces in the Five-Dimensional Heisenberg Group Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Willmore 2-Spheres in \(S^n\): A Survey

Authors : Xiang Ma, Peng Wang

Published in: Geometry and Topology of Manifolds

Publisher: Springer Japan

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Abstract

We give an overview of the classification problem of Willmore 2-spheres in \(S^n\), and report the recent progress on this problem when \(n=5\) (or even higher). We explain two main ingredients in our work. The first is the adjoint transform of Willmore surfaces introduced by the first author, which generalizes the dual Willmore surface construction. The second is the DPW method applied to Willmore surfaces whose conformal Gauss map is well-known to be a harmonic map into a non-compact symmetric space (a joint work of Dorfmeister and the second author). We also sketch a possible way to classify all Willmore 2-spheres in \(S^n\).

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previous chapter Some Evolution Problems in the Vacuum Einstein Equations
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Metadata
Title
Willmore 2-Spheres in : A Survey
Authors
Xiang Ma
Peng Wang
Copyright Year
2016
Publisher
Springer Japan
Book
Geometry and Topology of Manifolds

Print ISBN: 978-4-431-56019-7

Electronic ISBN: 978-4-431-56021-0

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-4-431-56021-0_12

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