Stability inequalities for Lawson cones

In [1], Guido De Philippis and Francesco Maggi proved global quadratic stability inequalities and derived explicit lower bounds for the first eigenvalues of the stability operators for all area-minimizing Lawson cones $M_{kh}$, except for those with\[(k, h), (h, k) \in S = \lbrace (3, 5), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11) \rbrace \; \textrm{.}\]We proved the corresponding inequalities and lower bounds for these Lawson cones $M_{kh}$ with $(k, h), (h, k) \in S$ by using different sub-calibrations from theirs, thus extending their results to all area-minimizing Lawson cones.

Keywords

Simons cones, Lawson cones

2010 Mathematics Subject Classification

53Bxx

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Dedicated to Xunjing Wei.

Received 6 December 2017

Accepted 16 November 2018

Published 3 August 2020