论文标题
高原流量或半谐波地图的热流
Plateau flow or the heat flow for half-harmonic maps
论文作者
论文摘要
Using the interpretation of the half-Laplacian on $S^1$ as the Dirichlet-to-Neumann operator for the Laplace equation on the ball $B$, we devise a classical approach to the heat flow for half-harmonic maps from $S^1$ to a closed target manifold $N$, recently studied by Wettstein, and for arbitrary finite-energy data we obtain a result fully analogous to the author's 1985 results for the harmonic地图表面的热流和类似的通用性。当$ n $是一种平稳嵌入，定向的封闭曲线$γ$时，半谐波地图热流可能被视为一种替代梯度流量，用于盘状最小表面的高原问题的变体。
Using the interpretation of the half-Laplacian on $S^1$ as the Dirichlet-to-Neumann operator for the Laplace equation on the ball $B$, we devise a classical approach to the heat flow for half-harmonic maps from $S^1$ to a closed target manifold $N$, recently studied by Wettstein, and for arbitrary finite-energy data we obtain a result fully analogous to the author's 1985 results for the harmonic map heat flow of surfaces and in similar generality. When $N$ is a smoothly embedded, oriented closed curve $Γ$ the half-harmonic map heat flow may be viewed as an alternative gradient flow for a variant of the Plateau problem of disc-type minimal surfaces.
