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#### A boundary Harnack principle in twisted Hölder domains

(Annals of Mathematics, 1991-09)

The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the set] (0, 1/2), there exists a twisted Hölder domain of order [alpha] for which the boundary Harnack principle ...

#### The Martin boundary in non-Lipschitz domains

(American Mathematical Society, 1993)

The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean
boundary in C [to the power of gamma] domains, where [gamma](x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.

#### Lifetimes of conditioned diffusions

(Springer-Verlag GmbH, 1992)

We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for each of the following classes of domains: L [to the power of p] domains (p = n − 1), uniformly regular twisted ...

#### Cutting Brownian Paths

(American Mathematical Society, 1999-01)

Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line
L is a cut line if there exists a time t [is an element of the set] (0, 1) such that the trace of {Z [subscript] s : 0 [is less than or equal to] s < t} lies on one side of L and the trace of {Z [subscript] s : t < s < 1} lies on the other ...