Degenerate complex Monge-Amp\`ere flows on strictly pseudoconvex domains

Hoang-Son Do

doi:10.1007/s00209-016-1838-z

Degenerate complex Monge-Amp\`ere flows on strictly pseudoconvex domains

Complex Variables 2019-11-26 v3

Authors: Hoang-Son Do

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Abstract

We study the equation $\dot{u}=\log\det (u_{\alpha\bar{\beta}})+f(t,z,u)$ in domains of $\mathbb C^n$ . This equation has a close connection with the K\"ahler-Ricci flow. In this paper, we consider the case of the boundary conditions are smooth and the initial conditions are bounded.

Keywords

complex monge-ampère equation pseudoconvex domains geodesic flow

Cite

@article{arxiv.1501.07167,
  title  = {Degenerate complex Monge-Amp\`ere flows on strictly pseudoconvex domains},
  author = {Hoang-Son Do},
  journal= {arXiv preprint arXiv:1501.07167},
  year   = {2019}
}

Comments

In this version, we fix a mistake in the condition of Theorem 0.1 (replace "\varphi(z,t)=u_0(z)" by "\varphi (z,0)=u_0(z)"). We also define \delta_m in the page 29 and correct a mistake in the page 30

Degenerate complex Monge-Amp\`ere flows on strictly pseudoconvex domains

Abstract

Keywords

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