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math.DG2023
Smoothness of conformal heat flow of harmonic maps
Woongbae Park
The conformal heat flow of harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global we…
math.DG2022★ 3 cited
A new conformal heat flow of harmonic maps
Woongbae Park
We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensiona…
math.DG2020
Compactness of harmonic maps of surfaces with regular nodes
Woongbae Park
In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a…