Alyssa Genschaw

activity

20182022

collaborators

4 papers

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…

math.AP2019

BMO Solvability and Absolute Continuity of Caloric Measure

Alyssa Genschaw, Steve Hofmann

We show that BMO-solvability implies scale invariant quantitative absolute continuity (specifically, the weak- $A_{\infty}$ property) of caloric measure with respect to surface measur…

math.AP2018

A Weak Reverse Holder Inequality for Caloric Measure

Alyssa Genschaw, Steve Hofmann

Following a result of Bennewitz-Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder inequality on an ope…