Alyssa Genschaw

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20182022

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math.CA2022

Lower bounds on Bourgain's constant for harmonic measure

Matthew Badger, Alyssa Genschaw

For every $n \geq 2$ , Bourgain's constant $b_{n}$ is the largest number such that the (upper) Hausdorff dimension of harmonic measure is at most $n - b_{n}$ for every domain in $\mathbb{R…

math.CA2021

Hausdorff dimension of caloric measure

Matthew Badger, Alyssa Genschaw

We examine caloric measures $ω$ on general domains in $R^{n + 1} = R^{n} \times R$ (space $\times$ time) from the perspective of geometric measure theory. On o…