Geometry of measures on smoothly stratified metric spaces
Jonathan C. MattinglyEzra MillerDo Tran
Jonathan C. MattinglyEzra MillerDo Tran
Nov 2023
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摘要原文
Any measure $\mu$ on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fr\'echet mean $\bar\mu$ yields a continuous "tangential collapse" from the tangent cone of M at $\bar\mu$ to a vector space that preserves the Fr\'echet mean, restricts to an isometry on the "fluctuating cone" of directions in which the Fr\'echet mean can vary under perturbation of $\mu$, and preserves angles between arbitrary and fluctuating tangent vectors at the Fr\'echet mean.
