Bo Berndtsson

2024

On the Ohsawa–Takegoshi Extension Theorem

Plurisubharmonic functions and real submanifolds of ℂⁿ

Long Geodesics in the Space of Kähler Metrics

Bergman kernels for Paley-Wiener spaces and Nazarov’s proof of the Bourgain-Milman theorem

ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES

Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem

Complex legendre duality

2020

Lelong Numbers and Vector Bundles

Complex interpolation of R-norms, duality and foliations

2019

Superforms, supercurrents, minimal manifolds and Riemannian geometry

Probability measures associated to geodesics in the space of kähler metrics

Complex Brunn-Minkowski theory and positivity of vector bundles

Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics

A comparison principle for bergman kernels

Real and complex Brunn-Minkowski theory

The volume of Kahler-Einstein varieties and convex bodies

A proof of the Ohsawa-Takegoshi theorem with sharp estimates

The Openness Conjecture and Complex Brunn-Minkowski Inequalities

A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry

2014

Symmetrization of Plurisubharmonic and Convex Functions

Convexity on the space of Kähler metrics

Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties

Quantitative extensions of pluricanonical forms and closed positive currents

L-2-Extension of partial derivative-closed form

A Brunn-Minkowski inequality for Fano manifolds

Strict and nonstrict positivity of direct image bundles

Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's "hypothèse fondamentale"

L^2-extensions of dbar-closed forms

Strict and non strict positivity of direct image bundles

Bergman kernels and subadjunction

Curvature of vector bundles associated to holomorphic fibrations

Probability measures related to geodesics in the space of Kähler metrics

Positivity of direct image bundles and convexity on the space of Kähler metrics.

A direct approach to Bergman kernel asymptotics for positive line bundles

A Bergman kernel proof of the Kawamata subadjunction theorem

An extension problem for convex functions

Bergman kernels and the pseudoeffectivity of relative canonical bundles

L 2 -estimates for the d-equation and Witten’s proof of the Morse inequalities

Positivity of direct image bundles and convexity on the space of Kahler metrics

Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

A remark on approximation on totally real sets

L2-estimates for the d-equation and Witten's Proof of the Morse Inequalities

Integral formulas and the Ohsawa-Takegoshi extension theorem

Curvature of Vector Bundles and Subharmonicity of Bergman Kernels

Curvature of Vector Bundles Associated to Holomorphic Fibrations

Subharmonicity Properties of the Bergman Kernel and Some Other Functions Associated to Pseudoconvex Domains

The Maximum Polygon Area and its Relation to the Isoperimetric Inequality

Integral Formulas and the Oshawa-Takegoshi Extension Theorem

Asymptotics of Bergman Kernels

Non-holomorphic functional calculus for commuting operators with real spectrum

Almost holomorphic extensions of ultradifferentiable functions