211 citations · 1.3k across the 126 of their papers we have counts for
9 papers · 1 filter
Real-analytic geodesics in the Mabuchi space of Kähler metrics and quantization
Alix Deleporte, Steve Zelditch
We prove the convergence of quantized Bergman geodesics to the Mabuchi geodesics for the initial value problem, in the case of real-analytic initial data and in short time. This pa…
Self-focal points of ellipsoids of dimension
Sean Gomes, Steve Zelditch
A self-focal point of a Riemannian manifold is a point so that every geodesic starting from returns to at some positive time. It is called a pole if all geodesi…
Topology of the nodal set of random equivariant spherical harmonics on
Junehyuk Jung, Steve Zelditch
We show that real and imaginary parts of equivariant spherical harmonics on have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is…
The Cauchy problem for the homogeneous Monge-Ampere equation, III. Lifespan
Yanir A. Rubinstein, Steve Zelditch
We prove several results on the lifespan, regularity, and uniqueness of solutions of the Cauchy problem for the homogeneous complex and real Monge-Ampere equations (HCMA/HRMA) unde…
The Cauchy problem for the homogeneous Monge-Ampere equation, I. Toeplitz quantization
Yanir A. Rubinstein, Steve Zelditch
The Cauchy problem for the homogeneous (real and complex) Monge-Ampere equation (HRMA/HCMA) arises from the initial value problem for geodesics in the space of Kahler metrics. It i…
On the Spectrum of geometric operators on Kähler manifolds
Dmitry Jakobson, Alexander Strohmaier, Steve Zelditch
On a compact Kähler manifold there is a canonical action of a Lie-superalgebra on the space of differential forms. It is generated by the differentials, the Lefschetz operator and…