20,414 research outputs found
On estimates for the equation in Stein manifolds
We generalize to intersection of strictly -convex domains in Stein
manifold, and Lipschitz estimates for the solutions of the equation done by Ma and Vassiliadou for domains in For this we use a Docquier-Grauert holomorphic retraction
plus the raising steps method I introduce earlier. This gives results in the
case of domains with low regularity, for their boundary.Comment: I follow the nice suggestions done by the referee which substantially
simplify the proof of theorem 4.1. Also typos are corrected and the
presenrtation is slightly modifie
Optimal Cobordisms between Torus Knots
We construct cobordisms of small genus between torus knots and use them to
determine the cobordism distance between torus knots of small braid index. In
fact, the cobordisms we construct arise as the intersection of a smooth
algebraic curve in with the unit 4-ball from which a 4-ball of
smaller radius is removed. Connections to the realization problem of
-singularities on algebraic plane curves and the adjacency problem for
plane curve singularities are discussed. To obstruct the existence of
cobordisms, we use Ozsv\'ath, Stipsicz, and Szab\'o's -invariant,
which we provide explicitly for torus knots of braid index 3 and 4.Comment: 24 pages, 7 figures. Version 3: Minor corrections, implementation of
referee's recommendations. Comments welcom
- …