90 citations · 153 across the 31 of their papers we have counts for
36 papers
Einstein four-manifolds of positive sectional curvature and ADM mass
Matthew Gursky, Andrea Malchiodi
We prove that closed Einstein four-manifolds with positive sectional curvature and Euler characteristic and signature satisfying must be homothetically…
Renormalized area of minimal surfaces in hyperbolic space
Matthew J. Gursky, Khoi Nguyen, Aaron J. Tyrrell
In this paper we consider minimal surfaces in hyperbolic space of arbitrary codimension that are critical for renormalized area. We give two criteria which imply that must be a…
Admissibility, Topology, and the -Loewner--Nirenberg problem
Hao Fang, Matthew J. Gursky
The -Loewner--Nirenberg problem is a fully nonlinear generalization of the classical Loewner--Nirenberg problem of constructing complete conformal metrics with constant negati…
Mass and volume of four-dimensional Einstein metrics
Matthew Gursky, Andrea Malchiodi
Let be an Einstein manifold, where is a smooth, closed, oriented four-manifold and has positive Einstein constant. Given a point ,…
Self-dual and even Poincaré-Einstein metrics in dimension four
Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré…
The Anti-Self-Dual Deformation Complex and a conjecture of Singer
A. Rod Gover, Matthew J. Gursky
Let be a smooth, closed, oriented anti-self-dual (ASD) four-manifold. is said to be unobstructed if the cokernel of the linearization of the self-dual Weyl tens…