arXiv subjects

Bowoo Kang

Publications and source records attributed to Bowoo Kang.

3 recordsLinked to original sources

arXiv2026

Weak Solutions to the complex Monge-Amp\`ere flows on compact K\"ahler manifolds : general measures on the right-hand side

We show the existence of a bounded solution to the Cauchy problem for the complex Monge-Amp\`ere flow on a compact K\"ahler manifold, with the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a H\"older continuous quasi-plurisubharmonic function. We also prove that for a given semi-positive big from $\theta$, the $t$-slice of the solution is locally H\"older continuous on $\rm{Amp(\theta)}$ for all $t \in (0, T)$. Next, we prove a comparison principle when $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded quasi-plurisubharmonic function, which implies the uniqueness of the solution.

math.CV↗

arXiv2025

A general comparison principle for the pluripotential complex Monge-Amp\`ere flow

We prove a comparison principle for the pluripotential complex Monge-Amp\`ere flows for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded plurisubharmonic function. As a consequence, we obtain the uniqueness of the weak solution to the pluripotential Cauchy-Dirichlet problem. We also study the long-term behavior of the solution under some assumption.

math.CV↗

arXiv2025

The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Amp\`ere flow with a general measure on the right-hand side

We show that the pluripotential Cauchy-Dirichlet problem for the complex Monge-Amp\`ere flow is solvable for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded plurisubharmonic function. In particular, we remove the strict positivity assumption on $d\mu$. We use this result to prove the parabolic version of the bounded subsolution theorem due to Kolodziej in pluripotential theory.

math.CV↗