THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACE EQUATION IN Sol_3, WITH POSSIBLE INFINITE BOUNDARY DATA

摘要

In this paper, we study the Dirichlet problem for the minimal surface equation in Sol_3 with possible infinite boundary data, where Sol_3 is the non-Abelian solvable 3-dimensional Lie group equipped with its usual left-invariant metric that makes it into a model space for one of the eight Thurston geometries. Our main result is a Jenkins-Serrin type theorem which establishes necessary and sufficient conditions for the existence and uniqueness of certain minimal Killing graphs with a non-unitary Killing vector field in Sol_3.