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    • Mathematics (MA)
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    On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds

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    Author
    Sivaram, P
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    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.
    URI
    https://etd.iisc.ac.in/handle/2005/6572
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    • Mathematics (MA) [163]

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