Octonionic Calabi-Yau theorem

DOI10.1007/s12220-024-01736-0MaRDI QIDQ6596295

Semyon Alesker, Peter V. Gordon

Publication date: 2 September 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

octonionsMonge-Ampère equationsCalabi-Yau theorem

Mathematics Subject Classification ID

Calabi-Yau theory (complex-analytic aspects) (32Q25) Monge-Ampère equations (35J96)

Cites Work

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• Dirichlet problem of quaternionic Monge-Ampère equations
• On a uniform estimate for the quaternionic Calabi problem
• Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric
• Pluripotential theory on quaternionic manifolds
• Quasicontinuity and maximality of quaternionic plurisubharmonic functions
• Dirichlet duality and the nonlinear Dirichlet problem on Riemannian manifolds
• Weak Spin(9)-structures on 16-dimensional Riemannian manifolds
• Plurisubharmonic functions on the octonionic plane and \(Spin (9)\)-invariant valuations on convex sets
• Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds
• Quaternionic determinants
• HKT and OKT geometries on soliton black hole moduli spaces
• Quaternionic Monge-Ampère equations
• The geometry of (super) conformal quantum mechanics
• Geometry of hyper-Kähler connections with torsion
• Elliptic partial differential equations of second order
• Twistor spaces for hyper-Kähler manifolds with torsion
• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables.
• A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)
• Regularity of solutions to the quaternionic Monge-Ampère equation
• The \(C^0\) estimate for the quaternionic Calabi conjecture
• The inhomogeneous Dirichlet problem for natural operators on manifolds
• The role of \(\mathrm{Spin}(9)\) in octonionic geometry
• On the quaternionic Monge-Ampère operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space
• Potential theory for quaternionic plurisubharmonic functions
• Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry
• Valuations on convex sets, non-commutative determinants, and pluripotential theory
• Zur Theorie der gemischten Volumina von konvexen Körpern. IV: Die gemischten Diskriminanten und die gemischten Volumina.
• Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a Spin(9)-structure
• Elliptic partial differential equations
• Lectures on exceptional Lie groups. Ed. by Zafer Mahmud and Mamoru Mimura
• The Calabi–Yau Theorem
• Finite Lorentz transformations, automorphisms, and division algebras
• Potentials for hyper-Kähler metrics with torsion
• The complex Monge-Ampère equation on compact Hermitian manifolds
• Division algebras, (pseudo)orthogonal groups and spinors
• An introduction to potential theory in calibrated geometry
• Dirichlet duality and the nonlinear Dirichlet problem
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The octonions
• The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations
• Convex Bodies The Brunn-MinkowskiTheory
• Quaternionic plurisubharmonic functions and their applications to convexity
• On the Alesker-Verbitsky conjecture on hyperKähler manifolds

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