Asian Journal of Mathematics

Volume 23 (2019)

Number 6

Stability inequalities for Lawson cones

Pages: 1001 – 1012



Zhenhua Liu (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)


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.


Simons cones, Lawson cones

2010 Mathematics Subject Classification


Dedicated to Xunjing Wei.

Received 6 December 2017

Accepted 16 November 2018

Published 3 August 2020