CV and papers.
You can get my CV
here.
Below is a list of my papers and preprints
together with a short description of each of them.
We study the problem of
conformal deformation of Riemannian structure to constant scalar
curvature with zero mean curvature on the boundary. We prove
compactness for the full set of solutions when the boundary is umbilic
and the dimension $n \leq 24$. The Weyl Vanishing Theorem is also
established under these hypothesis. Finally, we provide
counter-examples to compactness when $n \geq 25$.
Motion of Slightly Compressible Fluids in a Bounded Domain, with David G. Ebin. Pre-print. October 201. 48 pages.
We study the
initial-boundary value problem for equations of inviscid fluid motion
in a bounded domain in R^n. We show that the solution to this problem
for a slightly compressible fluid (or fluid with high sound speed) is
near to that of an incompressible fluid. We also prove that the
solution to the initial-value problem depends in a $C^1$ fashion on the
initial data. Such a dependence is unusual for non-linear equations.
In this
letter we prove that non-trivial compact Yamabe solitons or
breathers do not exist. In particular our proof in the two dimensional
case dependes only on properties of the determinant of the Laplacian
and turns out to be independent of the classical uniformization
theorem. Using this remarkable fact we are able to explain how the
uniformization theorem for Riemann surfaces can be obtained using the
Yamabe-Ricci flow.
In this work
we show that a certain family of Coupled Map Lattices
presents different asymptotic behaviors when some parameters (including
coupling) are changed. We proof that we can begin with a configuration
with infinitely many different measures and, with a slight change in
coupling, get an asymptotic state with only one measure describing the
behavior of most orbits. Since our results are motivated by some
results coming from physics, in order to establish a common language we
also give a non-technical introduction to the theory of invariant
measures and equilibrium in Dynamics.
Using
finite-time Lyapunov exponent we investigate the relations
between Unstable Dimension Variability and the phase space dimension.
A study is
developed focusing on the lost of stability of the interface
dividing two regions of different spatial patterns on a coupled map
lattice.
Notes.
Here are some notes that I (and other people) have taken.
Some algebraic
structures
in physics - notes from a series of informal
meetings that I and some other students organized with the goal of
sharing our different background in physics and mathematics (pdf file).
