Definition 4.15 ( C k , α -regularity scale) . [052L]

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Definition 4.15 ( $C^{k,\alpha}$ -regularity scale).

Let $(M^{n},g)$ be a Riemannian manifold with a $C^{k,\alpha}$ -Riemannian metric $g$ . The $C^{k,\alpha}$ -regularity scale at $p$ , denoted by $r_{k,\alpha}(p)$ , is defined as the supremum of all $r>0$ such that $M^{n}$ is $(r,k+\alpha,10^{-6})$ -regular at $p$ .

Definition 4.15 ( C k , α -regularity scale) . [052L]

Definition 4.15 (Ck,αC^{k,\alpha}-regularity scale).

Definition 4.15 ( $C^{k,\alpha}$ -regularity scale).