论文标题
RCD空间上的独特延续问题。我
Unique Continuation Problem on RCD Spaces. I
论文作者
论文摘要
在本说明中，我们建立了在紧凑型$ rcd（k，2）$空间上的弱独特延续定理，并表明存在$ rcd（k，4）$空间，在该空间上存在非凡的laplacian和非平台解决方案的非平凡特征，这些方程式的热量方程式消失了，从而消失至一点点。我们还建立了公制角上本征函数和热量功能的频率估计。特别是，这给出了强烈的独特延续类型，导致谐波函数的度量喇叭在喇叭尖处具有高衰减的谐波函数，在那里众所周知，标准强的独特连续性属性失败了。
In this note we establish the weak unique continuation theorem for caloric functions on compact $RCD(K,2)$ spaces and show that there exists an $RCD(K,4)$ space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point. We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails.
