论文标题
抛物线频率
Parabolic frequency on manifolds
论文作者
论文摘要
我们证明了抛物线频率在歧管上的单调性。这是Almgren频率函数的抛物线类似物。值得注意的是，我们在所有流形上都有单调性，并且不需要曲率假设。当歧管是欧几里得空间时，漂移操作员是Ornstein-Uhlenbeck操作员，这可以看到这意味着Poon对于普通热方程的频率单调性。频率的单调性是19世纪Hadamard的抛物线类似物三个圆圈定理，内容涉及$ \ cc $上的Holomorthic功能的对数凸度。从单调性来看，我们获得了抛物线独特的延续和向后的独特性。
We prove monotonicity of a parabolic frequency on manifolds. This is a parabolic analog of Almgren's frequency function. Remarkably we get monotonicity on all manifolds and no curvature assumption is needed. When the manifold is Euclidean space and the drift operator is the Ornstein-Uhlenbeck operator this can been seen to imply Poon's frequency monotonicity for the ordinary heat equation. Monotonicity of frequency is a parabolic analog of the 19th century Hadamard three circles theorem about log convexity of holomorphic functions on $\CC$. From the monotonicity, we get parabolic unique continuation and backward uniqueness.
