arXiv subjects
Publications and source records attributed to Peihe Wang.
We establish the existence of smooth solutions to the symmetric maximal surface equation with degenerate boundary conditions. Moreover, we prove that these solutions maximize the associated area functionals. This result serves as the Lorentzian analogue of minimal graphs in hyperbolic spaces together with their associated area minimizing problem.
In this paper, we study Hessian equations with prescribed contact angle boundary value or oblique derivative boundary value and finally derive the a priori global gradient estimate for the admissible solutions.
For the minimal graph defined on a convex ring in the space form with nonnegative curvature, we obtain the regularity and the strict convexity about its level sets by the continuity method.