29 citations · 60 across the 23 of their papers we have counts for
5 papers · 1 filter
The higher dimensional affine Bernstein and Plateau problems
Neil S. Trudinger, Xu-Jia Wang
In our previous papers [33, 34], we established the affine Bernstein theorem and proved the interior regularity for the affine Plateau problem in two dimensions. In this paper, we…
Boundary regularity for the Monge-Ampere and affine maximal surface equations
Neil S. Trudinger, Xu-Jia Wang
In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomogeneous term is only assumed to be Ho…
On Harnack inequalities and singularities of admissible metrics in the Yamabe problem
Neil S. Trudinger, Xu-Jia Wang
In this paper we study the local behaviour of admissible metrics in the k-Yamabe problem on compact Riemannian manifolds of dimension . For , we prove…
The Yamabe problem for higher order curvatures
Weimin Sheng, Neil S Trudinger, Xu-jia Wang
Let M be a compact Riemannian manifold of dimension n. The k-curvature, for k=1,2,..n, is defined as the k-th elementary symmetric polynomial of the eigenvalues of the Schouten ten…
The affine Plateau problem
Neil S. Trudinger, Xu-Jia Wang
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal sur…