Early
unpublished papers in hyperbolic geometry. Which have remained,
for some reason, unpublished. These are pdf files of scans of old typed
papers....they're from before I learned TeX. Displayed at full size
they are quite readable. Preprints of most of my
mathematical papers written after 2005 can be
found at the arXiv. Early
unpublished papers in hyperbolic geometry. Which have remained,
for some reason, unpublished. These are pdf files of scans of old typed
papers....they're from before I learned TeX. Displayed at full size
they are quite readable.
Joint papers with Richard
B.
Melrose:
We compute the index of a fourier integral operator defined by a
contact
diffeomorphism of a contact manifold. In MRL. Contact
degree and the index of Fourier integral
operators.
This is the long lost paper, Shrinking tubes
and the d-bar Neumann problem.
It's filled with tasty morsels, but it not recommeded for a single
sitting.
It contains a proof of the "The Boutet de Monvel-Guillemin" conjecture
as
well as the complete metric approach to the Bergmann kernel and a study
of the d-bar Neumann problem on shrinking Grauert tubes.
Joint papers with Gennadi
Henkin:
We consider strict complex cobordisms and embeddability for
3d CR-manifolds.
This paper includes an appendix by Bruno De Oliveira. In Proceedings of
the
Steklov Inst. (Corrected version of April 17, 2006) Can a good manifold come to a bad end?
This is a paper about embedding pseudoconcave manifolds and the stability of the algebra of CR-functions under deformations. In Acta Math. Stability of embeddings for pseudoconcave surfaces and their boundaries
Two local results about generically one to one analytic maps: Two lemmas in local analytic geometry
An expository paper on pseudoconcave manifolds and $L^2$-methods: Embedding 3-dimensional CR-manifolds
A note on the deformation theory of
open Stein manifolds. In CPDE. Deformations of
open Stein manifolds
Notes from lectures I gave at
CIRM, in
Luminy, France in June of 1999 on Toeplitz operators, index theorems
and
relative indices, revised in 2002 for the WHOI publication. Lectures on Indices and Relative Indices on
Contact
and CR-Manifolds
Notes from a lecture I gave in
December
1999 at the Conference on Several Complex Variables, Hayama, Japan. Filling pseudodoncave holes
A short paper correcting an
error in "A relative index on the space of embeddable CR-structures, I"
Ann. of Math. Erratum
Under the
same cohomologial hypotheses used in Stability of embeddings for
pseudoconcave surfaces and their boundaries,
I prove the conjecture that, among sufficiently small deformations of
the CR-structure on a strictly pseudoconvex, 3-manifold,
the relative index assumes only finitely many different values. Appears
in JIMJ. Geometric bounds on the relative
index
A short paper on convex
regions. Convex regions, shadows and the Gauss
map
A short paper on subelliptic
boundary conditions for the Spin-C Dirac operator on a complex
manifold: A priori estimates for a subelliptic
Spin-C
Dirac operator
A little note on the
convergence of the Neumann series in higher norms with applications to
the Marchenko equation (in CPDE): The convergence
of the
Neumann series in higher
norms.
A little note comparing the
finite Fourier transform to the Fourier transform (in CPAM): How well does the finite Fourier transform
approximate the Fourier transform?
Two papers on a careful
analysis of subelliptic boundary conditions for the Spin-C Dirac
operator and gluing formulae for holomorphic Euler characteristics on
partitioned compact, complex manifolds (in the Annals of
Math.):
This is part III. I extend the
subelliptic boundary conditions for the Spin-C Dirac operator to Spin_C
manifolds with almost complex boundaries. This leads to an
Agranovich-Dynin formula and a proof of formula for the relative
between two generalized Szego projectors. The Atiyah-Weinstein, on the
index of Fourier integral operator defined by a contact transformation
is a special case. I also get a very beautiful formula for the relative
index between two classical Szego projectors defined by embeddable
CR-structures on a contact 3-manifold, (in the Annals of Math.).
An expository account of my
work on sub-elliptic boundary value problems for the Spin_C Dirac
operator. In PNAS.
A short note with
Jack Morava on the analytic extension of the
polylogarithm functions, on the real line, as an entire family of
tempered distributions. Tempering the Polylog.
A paper with John Schotland,
where we analyze of the "inverse" of the Laplace, and Laplace-like
transforms: The Bad Truth About Laplace's
Transform, in SIAM review.
My first foray into magnetic
resonance imaging. This paper is about using inverse scattering to
design selective RF-pulses.
(final version appears in JMR) Minimum energy
pulse synthesis via the inverse scattering transform
A paper on magnetic resonance
imaging in inhomogeneous background fields. (appears in Inverse
Problems) Magnetic Resonance Imaging in
Inhomgeneous
Fields
A paper the convergence
properties of the hard pulse approximation for the 2x2 AKNS system
(Spin domain Bloch Equation) with Jeremy Magland (in Inverse Problems) The
hard pulse approximation for the 2x2 AKNS
system
An article, with Felix Wehrli,
on MRI for the Elsevier Encyclopedia on Mathematical Physics Magnetic Resonance Imaging
An article, with Jeremy
Magland, on finding missing uniformly spaced samples, when sampling on
a polar grid Ramp sampling and projection
reconstruction
Other preprints and reprints available by sending e-mail to CL Epstein cle@math.upenn.edu