144 citations · 420 across the 30 of their papers we have counts for
4 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…
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…