Journal of Differential Geometry

Sharp stability inequalities for the Plateau problem

G. De Philippis and F. Maggi

Full-text: Open access

Abstract

The validity of global quadratic stability inequalities for uniquely regular area minimizing hypersurfaces is proved to be equivalent to the uniform positivity of the second variation of the area. Concerning singular area minimizing hypersurfaces, by a “quantitative calibration” argument we prove quadratic stability inequalities with explicit constants for all the Lawson’s cones, excluding six exceptional cases. As a by-product of these results, explicit lower bounds for the first eigenvalues of the second variation of the area on these cones are derived.

Article information

Source
J. Differential Geom., Volume 96, Number 3 (2014), 399-456.

Dates
First available in Project Euclid: 20 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1395321846

Digital Object Identifier
doi:10.4310/jdg/1395321846

Mathematical Reviews number (MathSciNet)
MR3189461

Zentralblatt MATH identifier
1293.49103

Citation

De Philippis, G.; Maggi, F. Sharp stability inequalities for the Plateau problem. J. Differential Geom. 96 (2014), no. 3, 399--456. doi:10.4310/jdg/1395321846. https://projecteuclid.org/euclid.jdg/1395321846


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