ScalingStacks

Proposition 4.4. In the chart $U^{s}_{w}$ the average function $\bar{\phi}$ is convex, and on the shrinked chart $U^{s}_{w,\delta}$ it has a Lipschitz bound:

$$|\bar{\phi}|\leq C,\quad|\bar{\phi}(x)-\bar{\phi}(x^{\prime})|\leq C|x-x^{\prime}|.$$

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