On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds
Abstract
The thesis consists of two parts. In the first part of the thesis, we classify the
convergence behaviour of rotationally symmetric solutions to the modified J-flow
on the blow-up of the complex projective space at a point.
In the second part of the thesis, we adapt the PDE approach of Guo et al. to prove
an L∞ estimate for transverse complex Monge-Amp`ere equations on a homologically
orientable transverse Kahler manifolds. As an application, we obtain a purely PDE
proof of the regularity of Calabi-Yau cone metrics on Q-Gorenstein T-varieties.
Collections
- Mathematics (MA) [163]
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