We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domains which is a small deformations of a strictly linearly convex domain D ⊂ C with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for fol...

The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the spatial boundary is orthogonal to the foliation of the spacetime. Such a restriction is undesirable for both theoretical and computational reasons. We remove the orthog-onality assumption and show that it is more natural to focus on t...

The analysis of gravitational wave data may require greater accuracy than is afforded by the adiabatic approximation to the trajectory of and field produced by a particle moving in curved spacetime. Higher accuracy is available with a two-timescale approach using as an expansion parameter the ratio of orbital time to radiation reaction time. To avoid apparent divergences at large distances, the...

In this note we shall study the lifts of stable foliations of pseudo-Anosov diffeomorphism to certain infinite abelian covers. This is motivated, at least in part, by recent progress in understanding the ergodic properties of the analogous horocycle flows on infinite surfaces [3],[13]. Our aim is to show that many of the results from that context hold in this natural and technically simpler set...

Field activities in the Britannia Range (Transantarctic Mountains, Antarctica) highlighted new geological features around the so-called Byrd Glacier discontinuity. Recent field surveys revealed the occurrence of significant amounts of mediumto high-grade metamorphic rocks, intruded by abundant coarse-grained porphyritic granitoids. Most of the granitoids are deformed, with foliation parallel to...

Given a compact Riemannian manifold on which a compact Lie group acts by isometries, it is shown that there exists a Riemannian foliation whose leaf closure space is naturally isometric (as a metric space) to the orbit space of the group action. Furthermore, this isometry (and foliation) may be chosen so that a leaf closure is mapped to an orbit with the same volume, even though the dimension o...

A general definition of a clock is proposed, and the role of clocks in establishing temporal pre-conditions in quantum mechanical questions is critically discussed. The different status of clocks as used by theorists external to a system and as used by participant-observers within a system is emphasized. It is shown that the foliation of spacetime into instants of time is necessary to correctly...