We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded κ-fat open set (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded κ-fat open sets with respect to these processes with their E...

For any α ∈ (0, 2), a truncated symmetric α-stable process in R is a symmetric Lévy process in R with no diffusion part and with a Lévy density given by c|x| 1{|x|<1} for some constant c. In [24] we have studied the potential theory of truncated symmetric stable processes. Among other things, we proved that the boundary Harnack principle is valid for the positive harmonic functions of this proc...

The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal [1] in which quasilocal energy is derived from the Hamiltonian of spatially bounded gravitational systems. Three different classes of boundary surfaces for the Kerr slice are considered (constant radius surfaces, round spheres, and the ergosu...

For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geometry, and we study the change of geodesic coordinate maps.

The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primari...

Let A be a bounded subset of R. We give an upper bound on the volume of the symmetric difference of A and f(A) where f is a translation, a rotation, or the composition of both, a rigid motion. The volume is measured by the d-dimensional Hausdorff measure, which coincides with the Lebesgue measure for Lebesgue measurable sets. We bound the volume of the symmetric difference of A and f(A) in term...

More than 600 high resolution spectra of stars of spectral type F and later have been obtained in order to search for signatures of differential rotation in line profiles. In 147 stars the rotation law could be measured; 28 of them are found to be differentially rotating. Comparison to rotation laws in stars of spectral type A reveals that differential rotation sets in at the convection boundar...

A conservative irrational pseudo-rotation of the two-torus is semi-conjugate to the irrational rotation if and only if it has the property of bounded mean motion [1]. (Here ‘irrational pseudo-rotation’ means a toral homeomorphism with a unique and totally irrational rotation vector.) The aim of this note is to explore this concept some further. For instance, we provide an example which shows th...