m at h . A G ] 1 6 Ju n 20 08 REAL REGULATORS ON SELF - PRODUCTS OF K 3 SURFACES

ar X iv : 0 70 4 . 17 02 v 2 [ m at h . A G ] 2 6 Ju n 20 08 THE CANONICAL VOLUME OF 3 - FOLDS OF GENERAL TYPE WITH χ ≤ 0

We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.

ar X iv : m at h / 99 07 08 5 v 1 [ m at h . G R ] 1 3 Ju l 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS

ar X iv : m at h / 04 06 08 3 v 3 [ m at h . PR ] 1 7 Ju n 20 05 Large deviations for empirical entropies of g - measures

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.

ar X iv : 0 80 6 . 27 64 v 1 [ m at h - ph ] 1 7 Ju n 20 08 Self - adjoint extensions of Coulomb systems in 1 , 2 and 3 dimensions

We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in Rn, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly consid...

ar X iv : m at h / 03 03 37 7 v 2 [ m at h . G T ] 1 3 Ju n 20 03 ALMOST NORMAL HEEGAARD SURFACES

We present a new and shorter proof of Stocking's result that any strongly irreducible Heegaard surface of a closed orientable triangulated 3– manifold is isotopic to an almost normal surface. To make our paper essentially self-contained, we reprove a result of Jaco and Rubinstein on normal spheres, Scharlemann's " no nesting " lemma, and the fact that S 3 has no strongly irre-ducible Heegaard s...