60 citations · 402 across the 74 of their papers we have counts for
6 papers · 1 filter
On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign
Qing Han, Marcus Khuri
We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order…
The Local Isometric Embedding in R^3 of Two-Dimensional Riemannian Manifolds With Gaussian Curvature Changing Sign to Finite Order on a Curve
Marcus A. Khuri
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These two problems are: the local iso…
Local Solvability of a Class of Degenerate Monge-Ampere Equations and Applications to Geometry
Marcus A. Khuri
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally pre…
Counterexamples to the Local Solvability of Monge-Ampere Equations in the Plane
Marcus A. Khuri
In this paper, we present smooth examples of degenerate hyperbolic and mixed type Monge-Ampere equations in the plane, which do not admit a local C^3 solution.
On the Local Solvability of Darboux's Equation
Marcus A. Khuri
We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear eq…
Uniqueness of static vacuum Einstein metrics and the Bartnik quasi-local mass
Michael T. Anderson, Marcus A. Khuri
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructe…