Minimal surfaces: Variational theory and applications

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more remarkably, minimal surfaces (or minimal submanifolds) have encountered striking applications in other fields, like three-dimensional topology, mathematical physics, conformal geometry, among others. Even though it has been the subject of intense activity, many basic open problems still remain. In this lecture we will survey recent advances in this area and discuss some future directions. We will give special emphasis to the variational aspects of the theory as well as to the applications to other fields.

Original languageEnglish (US)
Title of host publicationPlenary Lectures and Ceremonies
EditorsSun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
PublisherKYUNG MOON SA Co. Ltd.
Pages283-310
Number of pages28
ISBN (Electronic)9788961058049
StatePublished - 2014
Event2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of
Duration: Aug 13 2014Aug 21 2014

Publication series

NameProceeding of the International Congress of Mathematicans, ICM 2014
Volume1

Conference

Conference2014 International Congress of Mathematicans, ICM 2014
CountryKorea, Republic of
CitySeoul
Period8/13/148/21/14

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Calculus of variations
  • Conformal geometry
  • Minimal surfaces
  • Three-manifold topology

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