563 research outputs found
Calibrations and isoperimetric profiles
We equip many non compact non simply connected surfaces with smooth
Riemannian metrics whose isoperimetric profile is smooth, a highly non generic
property. The computation of the profile is based on a calibration argument, a
rearrangement argument, the Bol-Fiala curvature dependent inequality, together
with new results on the profile of surfaces of revolution and some hardware
know-how.Comment: To appear soon in American Journal of Mathematics, a journal
published by The Johns Hopkins University Pres
Smooth embeddings with Stein surface images
A simple characterization is given of open subsets of a complex surface that
smoothly perturb to Stein open subsets. As applications, complex 2-space C^2
contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and
others homotopy equivalent to the 2-sphere but cut out by smooth, compact
3-manifolds. Pseudoconvex embeddings of Brieskorn spheres and other 3-manifolds
into complex surfaces are constructed, as are pseudoconcave holomorphic
fillings (with disagreeing contact and boundary orientations). Pseudoconcave
complex structures on Milnor fibers are found. A byproduct of this construction
is a simple polynomial expression for the signature of the (p,q,npq-1) Milnor
fiber. Akbulut corks in complex surfaces can always be chosen to be
pseudoconvex or pseudoconcave submanifods. The main theorem is expressed via
Stein handlebodies (possibly infinite), which are defined holomorphically in
all dimensions by extending Stein theory to manifolds with noncompact boundary.Comment: 26 pages, 1 figure. Version 2 has minor stylistic changes for
clarity, remark expanded at end of Section 4; accepted for publication by the
Journal of Topolog
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