One dimensional conformal metric flow II
Yilong Ni, Meijun Zhu
TL;DR
This paper studies one-dimensional conformal metric flows, focusing on fourth-order evolution equations, and establishes global existence and exponential convergence results for the 1-Q and 4-Q flows.
Contribution
It advances understanding of conformal metric flows by proving global existence and exponential convergence for specific fourth-order flows in one dimension.
Findings
Global existence of solutions for 1-Q and 4-Q flows
Exponential convergence of metrics under these flows
Extension of previous studies to higher-order derivatives
Abstract
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Geometry and complex manifolds