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Geometric and Functional Analysis

, Volume 25, Issue 4, pp 1240–1257 | Cite as

Some remarks on stability of cones for the one-phase free boundary problem

  • David JerisonEmail author
  • Ovidiu Savin
Article

Abstract

We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension 4. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension 4.

Keywords

Free Boundary Minimal Surface Free Boundary Problem Stable Cone Strict Subsolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsCambridgeUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA

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