Bo Berndtsson

2024

On the Ohsawa–Takegoshi Extension Theorem

Plurisubharmonic functions and real submanifolds of ℂⁿ

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

ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES

Long Geodesics in the Space of Kähler Metrics

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

2020

Lelong Numbers and Vector Bundles

Complex interpolation of R-norms, duality and foliations

Complex legendre duality

2019

Superforms, supercurrents, minimal manifolds and Riemannian geometry

Complex Brunn-Minkowski theory and positivity of vector bundles

Probability measures associated to geodesics in the space of kähler metrics

The volume of Kahler-Einstein varieties and convex bodies

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

Real and complex Brunn-Minkowski theory

A comparison principle for bergman kernels

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

L-2-Extension of partial derivative-closed form

Quantitative extensions of pluricanonical forms and closed positive currents

A Brunn-Minkowski inequality for Fano manifolds

L^2-extensions of dbar-closed forms

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

Strict and nonstrict positivity of direct image bundles

Strict and non strict positivity of direct image bundles

Bergman kernels and subadjunction

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

Probability measures related to geodesics in the space of Kähler metrics

Curvature of vector bundles associated to holomorphic fibrations

A Bergman kernel proof of the Kawamata subadjunction theorem

A direct approach to Bergman kernel asymptotics for positive line bundles

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

A remark on approximation on totally real sets

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

Curvature of Vector Bundles Associated to Holomorphic Fibrations

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

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

Asymptotics of Bergman Kernels

The Maximum Polygon Area and its Relation to the Isoperimetric Inequality

Integral formulas and the Ohsawa-Takegoshi extension theorem

Integral Formulas and the Oshawa-Takegoshi Extension Theorem

Curvature of Vector Bundles and Subharmonicity of Bergman Kernels

Non-holomorphic functional calculus for commuting operators with real spectrum

Almost holomorphic extensions of ultradifferentiable functions