TY - JOUR

T1 - Bubbling with L 2-Almost Constant Mean Curvature and an Alexandrov-Type Theorem for Crystals

AU - Delgadino, Matias G.

AU - Maggi, Francesco

AU - Mihaila, Cornelia

AU - Neumayer, Robin

N1 - Funding Information:
RN supported by the NSF Graduate Research Fellowship under Grant DGE-1110007. FM, RN, andCMsupported by the NSF Grants DMS-1565354 and DMS-1361122. F. Maggi: On leave from the University of Texas at Austin. The authors declare that they have no conflict of interest.
Funding Information:
Funding: RN supported by the NSF Graduate Research Fellowship under Grant DGE-1110007. FM, RN, and CM supported by the NSF Grants DMS-1565354 and DMS-1361122.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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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U2 - 10.1007/s00205-018-1267-8

DO - 10.1007/s00205-018-1267-8

M3 - Article

AN - SCOPUS:85049851742

VL - 230

SP - 1131

EP - 1177

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 3

ER -