Smooth approximation of the modified conical K\"ahler-Ricci flow

TL;DR

This paper introduces a modified conical K"ahler-Ricci flow incorporating a holomorphic vector field and constructs its long-term solution as a limit of smooth flows, advancing understanding of geometric flows with singularities.

Contribution

It presents a novel modification of the conical K"ahler-Ricci flow using a holomorphic vector field and establishes a method to obtain long-time solutions via smooth approximations.

Findings

Constructed long-time solutions as limits of smooth flows

Extended the theory of conical K"ahler-Ricci flows

Provided a new approach to flows with singularities

Abstract

We introduce the conical K\"ahler-Ricci flow modified by a holomorphic vector field. We construct a long-time solution of the modified conical K\"ahler-Ricci flow as the limit of a sequence of smooth K\"ahler-Ricci flows.