Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric

Semyon Alesker

doi:10.1016/j.aim.2013.03.021

Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric

Semyon Alesker

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

A quaternionic version of the Calabi problem was formulated by Alesker and Verbitsky (2010). [6]. It conjectures a solvability of a quaternionic Monge-Ampère equation on a compact HKT manifold (HKT stays for HyperKähler with Torsion). In this paper this problem is solved under the extra assumption that the manifold admits a flat hyperKähler metric compatible with the underlying hypercomplex structure. The proof uses the continuity method and a priori estimates.

Original language	English
Pages (from-to)	192-219
Number of pages	28
Journal	Advances in Mathematics
Volume	241
DOIs	https://doi.org/10.1016/j.aim.2013.03.021
State	Published - Jul 2013

Keywords

Calabi type problem
Monge-Ampère equations
Quaternions

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2013.03.021

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title = "Solvability of the quaternionic Monge-Amp{\`e}re equation on compact manifolds with a flat hyperK{\"a}hler metric",

abstract = "A quaternionic version of the Calabi problem was formulated by Alesker and Verbitsky (2010). [6]. It conjectures a solvability of a quaternionic Monge-Amp{\`e}re equation on a compact HKT manifold (HKT stays for HyperK{\"a}hler with Torsion). In this paper this problem is solved under the extra assumption that the manifold admits a flat hyperK{\"a}hler metric compatible with the underlying hypercomplex structure. The proof uses the continuity method and a priori estimates.",

keywords = "Calabi type problem, Monge-Amp{\`e}re equations, Quaternions",

author = "Semyon Alesker",

note = "Funding Information: This research was partially supported by ISF grants 701/08 and 1447/12 .",

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PY - 2013/7

Y1 - 2013/7

N2 - A quaternionic version of the Calabi problem was formulated by Alesker and Verbitsky (2010). [6]. It conjectures a solvability of a quaternionic Monge-Ampère equation on a compact HKT manifold (HKT stays for HyperKähler with Torsion). In this paper this problem is solved under the extra assumption that the manifold admits a flat hyperKähler metric compatible with the underlying hypercomplex structure. The proof uses the continuity method and a priori estimates.

AB - A quaternionic version of the Calabi problem was formulated by Alesker and Verbitsky (2010). [6]. It conjectures a solvability of a quaternionic Monge-Ampère equation on a compact HKT manifold (HKT stays for HyperKähler with Torsion). In this paper this problem is solved under the extra assumption that the manifold admits a flat hyperKähler metric compatible with the underlying hypercomplex structure. The proof uses the continuity method and a priori estimates.

KW - Calabi type problem

KW - Monge-Ampère equations

KW - Quaternions

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DO - 10.1016/j.aim.2013.03.021

M3 - مقالة

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VL - 241

SP - 192

EP - 219

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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