Journal of Differential Geometry

Sharp stability inequalities for the Plateau problem

G. De Philippis and F. Maggi

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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.

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

First available in Project Euclid: 20 March 2014

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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.

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