61 citations · 233 across the 26 of their papers we have counts for
6 papers · 1 filter
Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry
Tamás Darvas, Chinh H. Lu
We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature Kähler metrics. We carry this out by explori…
metric geometry of big and nef cohomology classes
Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold of dimension , and be a closed smooth real -form representing a big and nef cohomology class. We introduce a metric $d_p, p\g…
Pluripotential Theory and Convex Bodies: Large Deviation Principle
Turgay Bayraktar, Thomas Bloom, Norman Levenberg +1
We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in . Our goal is t…
Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold. We prove the existence and uniqueness of solutions to complex Monge-Ampère equations with prescribed singularity type. Compared to previou…
Quantization in geometric pluripotential theory
Tamás Darvas, Chinh H. Lu, Yanir A. Rubinstein
The space of Kähler metrics can, on the one hand, be approximated by subspaces of algebraic metrics, while, on the other hand, can be enlarged to finite-energy spaces arising in pl…
L^1 metric geometry of big cohomology classes
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Suppose is a compact Kähler manifold of dimension , and is closed -form representing a big cohomology class. We introduce a metric on the finite energy…