Archive for Rational Mechanics and Analysis

, Volume 230, Issue 3, pp 1131–1177 | Cite as

Bubbling with L2-Almost Constant Mean Curvature and an Alexandrov-Type Theorem for Crystals

  • Matias G. Delgadino
  • Francesco MaggiEmail author
  • Cornelia Mihaila
  • Robin Neumayer


A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems.


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RN supported by the NSF Graduate Research Fellowship under Grant DGE-1110007. FM, RN, andCMsupported by the NSF Grants DMS-1565354 and DMS-1361122.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of MathematicsThe University of Texas at AustinAustinUSA
  3. 3.Department of MathematicsUniversity of ChicagoChicagoUSA
  4. 4.Department of MathematicsNorthwestern UniversityEvanstonUSA

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