2016/05/30 by Sargent, Pam · 1 citation
#37B30 #47A75 #49Q05 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1605.09143
In this paper, we give a relationship between the eigenvalues of the Hodge Laplacian and the eigenvalues of the Jacobi operator for a free boundary minimal hypersurface of a Euclidean convex body. We then use this relationship to obtain new index bounds for such minimal hypersurfaces in terms of their topology. In particular, we show that the index of a free boundary minimal surface in a convex domain in ℝ3 tends to infinity as its genus or the number of boundary components tends to infinity.