Then-dimensional analogue of the catenary: existence and nonexistence
Ulrich Dierkes, Gerhard Huisken · Pacific Journal of Mathematics · 1990
We study "heavy" A?-dimensional surfaces suspended from some prescribed (n -1) -dimensional boundary data.This leads to a mean curvature type equation with a non-monotone right hand side.We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data.