Finiteness of disjoint minimal graphs
Peter Li, Jiaping Wang · Mathematical Research Letters · 2001
nd was used to prove a structural theorem for harmonic maps. It turns out that this argument can also be use to study disjoint minimal graphs. Indeed, the purpose of this note is to show that there are only finitely many minimal graphs supported on disjoint open subsets in R n . Moreover, we will prove that the maximum possible number of such disjointly supported minimal graphs is (n+1)2 n . We would like to point out that it is somewhat surprising that the finiteness theorem is valid without any assumption on the growth rate of the defining functions. 1 Research partially supported by NSF grant #DMS-9971418 and an Earmarked grant of Hong Kong. 2 Research partially supported by NSF grant #DMS-0072181. 1 2 PETER LI AND JIAPING WANG After we communicated with Rosenberg of our result, he informed us that Spruck has recently proved that the number of disjoint sublinear growth