Jesse Ratzkin
Research
My research lies in the areas of geometric analysis and Riemannian
geometry concentrating on geometric variational problems. Many of
the problems I study deal with noncompact manifolds or singularities
in an inescapable way.Also, the geometry and analysis are deeply
intertwined.
This is a picture of a 4-ended, coplanar CMC surfaces with 4-fold
symmetry, which Nick Schmitt generated using his program CMCLab:
You can read my CV, my
research statement, and
my teaching statement (all in
pdf format).
Publications and Preprints
The linked files below are all in PDF format.
- A Faber-Krahn eigenvalue estimate for wedge domains
on spheres, joint with
A. Treibergs. preprint.
- Coplanar, genus zero, CMC surfaces are nondegenerate, joint with
K.
Grosse-Brauckmann, N.
Korevaar, R.
Kusner, and
J. Sullivan. perprint.
- A Capture Problem in Brownian
Motion and Eigenvalues of Spherical Domains, joint with
Andrejs Treibergs,
to appear. Consider n Brownian cops
chasing one Brownian thief with all motion restricted to a line.
We find how many cops you need so that
the expected capture time of the thief is finite.
- On the Nondegeneracy of Constant Mean
Curvature Surfaces, joint with
Nick Korevaar and Rob
Kusner, Geom. Funct. Anal. 16:891--923, 2006.
earlier version here. in case you're
looking from a non-academic site. This paper gives a general
bound for the space of L^2 Jacobi fields on a coplanar, genus zero CMC
surface. In particular, we show almost all triunduloids are nondegenerate
(i.e. have no L^2 Jacobi fields).
-
An End to End Gluing Construction
for Metrics of Constant Positive Scalar Curvature Indiana Univ. Math. J.
Vol. 52 (2003), pg. 703--726. earlier
version, in case you're looking from a non-academic site.
- An End-to-End Gluing Construction
for Constant Mean Curvature Surfaces PhD Thesis, 2001
Lecture Notes
Math Circle notes: notes for a series of three lectures on
fractals, geared towards motivated high school students. Lecture 1. Lectures 2 and 3. Nick Korevaar wrote the
supporting MAPLE code.
Constant mean curvature
surfaces. These are lecture notes for a series of 4 lectures Nick,
Nat, Andrejs and I gave on constant mean curvature during a minicourse
in the summer of 2002.
Teaching
Math 2500 students click here
(both sections). Math 5200/7200 students click
here.
Previous courses:
- at the University of Georgia:
- at the University of Connecticut:
- Writing in Mathematics:
Math 200/201, Spring 2007
- Honors Differential Equations:
Math 221, Spring 2007
- Multivariable Calculus:
Math 210, Fall 2006
- Single Variable Calculus:
Math 115, Fall 2006
- Complex Analysis:
Math 252, Spring 2006
- Ordinary Differential Equations:
Math 211, Spring 2006
- Multivariable Calculus:
Math 210, Fall 2005
- Multivariable Calculus:
Math 210, Spring 2005
- Geometry: Math 223, Spring 2005
- Single Variable Calculus: Math 115,
Fall 2004
- Geometry: Math 223,
Fall 2004
- at the University of Utah:
Unfortunately, I don't have early courses archived.
Some Mathematical Links:
- The Geometry, Analysis, Numerics
and Graphics Program: They have a lot of neat pictures of minimal
and constant mean curvature surfaces. Also, they have several faculty
who work on problems closely related to those I think about.
- The minimal surfaces group
at Granada does great work and has a fantastic list of links and
preprints on their site.
- Math Preprints This
is a great resource for math articles. Anything that gets posted here
stays forever, so you can download preprint versions of papers going
back to 1994 (or so). And all the Annals articles get posted
here.
- Mathscinet has
references and reviews to articles going back to the early 1900's
- Dan
Pollack was my advisor. Ok, he still gives me advice; but it's a
less formal arrangement now.
The requisite list of links which have nothing to do with math.
Jesse Ratzkin jratzkin@math.uga.edu