Year: 2014
Author: Vamsi P. Pingali
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 333–346
Abstract
We consider a generalised complex Monge-Ampère equation on a compact Kähler manifold and treat it using the method of continuity. For complex surfaces we prove an existence result. We also prove that (for three-folds and a related real PDE in a ball in R^3) as long as the Hessian is bounded below by a pre-determined constant (whilst moving along themethod of continuity path), a smooth solution exists. Finally, we prove existence for another real PDE in a 3-ball, which is a local real version of a conjecture of X. X. Chen.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v27.n4.4
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 333–346
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Monge-Ampère equations
Author Details
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Hessian Equations of Krylov Type on Kähler Manifolds
Chen, Li
The Journal of Geometric Analysis, Vol. 33 (2023), Iss. 10
https://doi.org/10.1007/s12220-023-01394-8 [Citations: 0]