3 papers
math.CV2026
Ellipsoids in pseudoconvex domains II
Laszlo Lempert
We consider families of pseudoconvex domains parametrized by complex manifolds , and the maximal hermitian ellipsoids inscribed in each . The pap…
math.CV2026
Ellipsoids in pseudoconvex domains
Laszlo Lempert
We consider the problem of maximizing the volume of hermitian ellipsoids inscribed in a given pseudoconvex domain in complex Euclidean space. We prove existence and uniqueness, and…
math.CV2024
Two variational problems in Kähler geometry
Laszlo Lempert
On a Kähler manifold we consider the problems of maximizing/minimizing Monge--Ampère energy over certain subsets of the space of Kähler potentials. Under suitable assumptions we…