Reese Pathak

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math.MG2026

Optimal mean width and metric entropy estimates for convex bodies

Grigoris Paouris, Reese Pathak

We show that there exists a constant $C > 0$ such that for any $n \geq 1$ and any convex body $K \subset R^{n}$ , \[ 1 \leq \inf_{T \in \mathrm{GL}(n)} \, \frac{M^\ast(TK)}{\…

math.MG2026

On the metric projection onto a convex set: reverse HÃ¶lder inequalities and upper bounds

Reese Pathak

We study the $L^{p} (I^¼)$ -norm of the metric projection onto a closed, convex set $C \subset R^{n}$ when $I^¼$ is the uniform measure on the sphere or the standard Gaussian meas…