7 papers
A decade of metric geometry in the space of Kähler metrics
Tamás Darvas
We survey selected developments in the metric geometry of the space of Kähler metrics, emphasizing results from the past decade, highlighting open problems along the way.
The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds
Tamás Darvas, Mingchen Xia
We introduce the trace operator for quasi-plurisubharmonic functions on compact Kähler manifolds, allowing to study the singularities of such functions along submanifolds where th…
Lines in the space of Kähler metrics
Tamás Darvas, Nicholas McCleerey
We establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. We construct a wide range of weak geodesic lines on arbitrary…
Sharp estimates in Kähler quantization and non-pluripolar Radon measures
Zbigniew BÅocki, Tamás Darvas
Let denote the weighted Bergman kernel associated to a plurisubharmonic function . We obtain upper bounds and positive lower bounds for the Bergman metric $i\partial \ba…
Transcendental Okounkov bodies
Tamás Darvas, Rémi Reboulet, David Witt Nyström +2
We show that the volume of transcendental big -classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-MustaÅ£Ä and De…
A YTD correspondence for constant scalar curvature metrics
Tamás Darvas, Kewei Zhang
Given a compact Kähler manifold, to better understand Mabuchi's energy we introduce a family of energies, whose favorable properties are similar to those of the Ding en…