Corollary 5.12 . [04ET]

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Corollary 5.12.

(Volume lower bound) If $P$ is in the support of $L$ , then there is a uniform lower bound on the volume of $L$ inside Eulidean coordinate balls of radius less than $R$ :

\text{Vol}_{g}(L\cap B(P,r))\geq C^{-1}r^{n},\quad\forall r\leq R.

(56)