论文标题
曲线缩短流动流的圆锥形奇异性
Curve shortening flow on Riemann surfaces with conical singularities
论文作者
论文摘要
我们研究具有许多共形圆锥形奇点的黎曼表面上的曲线缩短流。如果初始曲线通过奇异点，则演变由退化的准抛物线方程来控制。在这种情况下，我们建立了短时间的存在，独特性和流量的规律性。我们还表明，不断发展的曲线保持固定在表面的单数点上，并获得了一些崩溃和收敛的结果。
We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evolution is governed by a degenerate quasilinear parabolic equation. In this case, we establish short time existence, uniqueness, and regularity of the flow. We also show that the evolving curves stay fixed at the singular points of the surface and obtain some collapsing and convergence results.
