Tam'as Darvas

activity

20122026

most citedTian's properness conjectures and Finsler geometry of the space of Kahler metrics

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

collaborators

42 papers

math.DG2026

Understanding entropy using Aubin--Yau deformations

Tamás Darvas, Kewei Zhang

In this paper we investigate three types of entropy that frequently appear in the research of Kähler geometry: the classical Kähler entropy, the radial entropy and the non-Archimed…

math.DG2026

Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants

Tamás Darvas, Kewei Zhang

We establish a Demailly-Kollár type continuity theorem for plurisubharmonic functions with respect to adapted measures on normal complex analytic klt pairs. As applications, we pro…

math.DG2026

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.

math.DG2026

Sharp $C^{1, 1 ˉ}$ estimates in Kähler quantization and non-pluripolar Radon measures

Zbigniew Błocki, Tamás Darvas

Let $K_{φ}$ denote the weighted Bergman kernel associated to a plurisubharmonic function $φ$ . We obtain upper bounds and positive lower bounds for the Bergman metric $i\partial \bar{…

math.DG2025

A YTD correspondence for constant scalar curvature metrics

Tamás Darvas, Kewei Zhang

Given a compact Kähler manifold, to better understand Mabuchi's $K$ energy we introduce a family of $K^{β}$ energies, whose favorable properties are similar to those of the Ding ener…

math.DG2025

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 pr…

math.CV2024

The Hausdorff distance and metrics on toric singularity types

Ayo Aitokhuehi, Benjamin Braiman, David Owen Horace Cutler +6

Given a compact Kähler manifold $(X, ω)$ , due to the work of Darvas-Di Nezza-Lu, the space of singularity types of $ω$ -psh functions admits a natural pseudo-metric $d_{S}$ th…

math.DG2024

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 the…

math.DG2023

Transcendental Okounkov bodies

Tamás Darvas, Rémi Reboulet, David Witt Nyström +2

We show that the volume of transcendental big $(1, 1)$ -classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-Mustaţă and Deng.…

math.DG2023

Extremizers of the $J$ functional with respect to the $d_{1}$ metric

Sam Bachhuber, Aaron Benda, Benjamin Christophel +1

In previous work, Darvas-George-Smith obtained inequalities between the large scale asymptotic of the $J$ functional with respect to the $d_{1}$ metric on the space of toric Kähler m…

math.CV2023★ 2 cited

Relative pluripotential theory on compact Kähler manifolds

Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu

Given a compact Kähler manifold, we survey the study of complex Monge-Ampère type equations with prescribed singularity type, developed by the authors in a series of papers. In add…

math.AG2023★ 1 cited

A transcendental approach to non-Archimedean metrics of pseudoeffective classes

Tamás Darvas, Mingchen Xia, Kewei Zhang

We introduce the concept of non-Archimedean metrics attached to a transcendental pseudoeffective cohomology class on a compact Kähler manifold. This is obtained via extending the R…

math.DG2022★ 3 cited

Twisted Kähler-Einstein metrics in big classes

Tamás Darvas, Kewei Zhang

We prove existence of twisted Kähler-Einstein metrics in big cohomology classes, using a divisorial stability condition. In particular, when $- K_{X}$ is big, we obtain a uniform Yau-…

math.DG2021★ 3 cited

The volume of pseudoeffective line bundles and partial equilibrium

Tamás Darvas, Mingchen Xia

Let $(L, h e^{- u})$ be a pseudoeffective line bundle on an $n$ -dimensional compact Kähler manifold $X$ . Let $h^{0} (X, L^{k} \otimes I (k u))$ be the dimension of the space of sectio…

math.DG2021

The Mabuchi geometry of low energy classes

Tamás Darvas

Let $(X, ω)$ be a Kähler manifold and $ψ : R \to R_{+}$ be a concave weight. We show that $H_{ω}$ admits a natural metric $d_{ψ}$ whose completion is the low energy spac…

math.DG2021

Optimal asymptotic of the $J$ functional with respect to the $d_{1}$ metric

Tamás Darvas, Erin George, Kevin Smith

We obtain sharp inequalities between the large scale asymptotic of the $J$ functional with respect to the $d_{1}$ metric on the space of Kahler metrics. Applications regarding the in…

math.DG2020★ 10 cited

The closures of test configurations and algebraic singularity types

Tamás Darvas, Mingchen Xia

Given a Kähler manifold $X$ with an ample line bundle $L$ , we consider the metric space of $L^{1}$ geodesic rays associated to the first Chern class $c_{1} (L)$ . We characterize rays th…

math.DG2019★ 3 cited

Griffiths extremality, interpolation of norms, and Kähler quantization

Tamás Darvas, Kuang-Ru Wu

Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is c…

math.DG2019

The metric geometry of singularity types

Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu

Let $X$ be a compact Kähler manifold. Given a big cohomology class ${θ}$ , there is a natural equivalence relation on the space of $θ$ -psh functions giving rise to $\mathcal S(X,θ…

math.DG2019

The isometries of the space of Kähler metrics

Tamás Darvas

Given a compact Kähler manifold, we prove that all global isometries of the space of Kähler metrics are induced by biholomorphisms and anti-biholomorphisms of the manifold. In part…

math.DG2019

Geometric pluripotential theory on Kähler manifolds

Tamás Darvas

Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Ampère type arising in Kähler geometry. Recently it has been discovered that m…

math.DG2018

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…

math.DG2018★ 39 cited

Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity

Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu

Let $(X, ω)$ 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…

math.DG2018

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…

Understanding entropy using Aubin--Yau deformations

Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants

A decade of metric geometry in the space of Kähler metrics

Sharp C1,1ˉ estimates in Kähler quantization and non-pluripolar Radon measures

A YTD correspondence for constant scalar curvature metrics

Lines in the space of Kähler metrics

The Hausdorff distance and metrics on toric singularity types

The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds

Transcendental Okounkov bodies

Extremizers of the J functional with respect to the d1​ metric

Relative pluripotential theory on compact Kähler manifolds

A transcendental approach to non-Archimedean metrics of pseudoeffective classes

Twisted Kähler-Einstein metrics in big classes

The volume of pseudoeffective line bundles and partial equilibrium

The Mabuchi geometry of low energy classes

Optimal asymptotic of the J functional with respect to the d1​ metric

The closures of test configurations and algebraic singularity types

Griffiths extremality, interpolation of norms, and Kähler quantization

The metric geometry of singularity types

The isometries of the space of Kähler metrics

Geometric pluripotential theory on Kähler manifolds

Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry

Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity

Quantization in geometric pluripotential theory

Sharp $C^{1, 1 ˉ}$ estimates in Kähler quantization and non-pluripolar Radon measures

Extremizers of the $J$ functional with respect to the $d_{1}$ metric

Optimal asymptotic of the $J$ functional with respect to the $d_{1}$ metric