Stability of the minimal surface system and convexity of area functional

Yng-Ing Lee, Mao-Pei Tsui
2014 Transactions of the American Mathematical Society  
We study the convexity of the area functional for the graphs of maps with respect to the singular values of their differentials. Suppose that f is a solution to the Dirichlet problem for the minimal surface system and the area functional is convex at f . Then the graph of f is stable. New criteria for the stability of minimal graphs in any co-dimension are derived in the paper by this method. Our results in particular generalize the co-dimension one case, and improve the condition in the 2003
more » ... per of the first author and M.-T. where p is an upper bound of the rank of df , and the condition in the 2008 paper of the first author and M.-T. Wang from det(I + (df ) T df ) ≤ 43 40 to det(I + (df ) T df ) ≤ 2.
doi:10.1090/s0002-9947-2014-06223-5 fatcat:q5nco7sgjrhgvpljehhegc5ope