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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 37, Issue 4


Enclosure theorems and barrier principles for energy stationary currents and the associated Brakke-flow

Patrick Henkemeyer
Published Online: 2017-10-31 | DOI: https://doi.org/10.1515/anly-2017-0048


We discuss certain quantitative geometric properties of energy stationary currents describing minimal surfaces under gravitational forces. Enclosure theorems give statements about the confinement of the support of currents to certain enclosing sets on the basis that one knows something about the position of their boundaries. These results are closely related to non-existence theorems for currents with connected support. Finally, we define a weak formulation in the theory of varifolds for the curvature flow associated to this energy functional. We extend the enclosure results to the flow and discuss several comparison principles.

Keywords: Geometric measure theory; variational problems in a geometric measure-theoretic setting, geometric evolution equations; currents

MSC 2010: 49Q15; 49Q20; 53C44; 58A25


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About the article

Received: 2017-09-20

Accepted: 2017-09-21

Published Online: 2017-10-31

Published in Print: 2017-11-01

The project was supported by the Studienstiftung des deutschen Volkes and Stanford University, where parts of this paper have been worked out.

Citation Information: Analysis, Volume 37, Issue 4, Pages 223–241, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2017-0048.

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