An evolving surface is a mean curvature flow if the normal
component of its velocity field is given by the mean curvature.
First introduced in the physics literature in the 1950s, the mean
curvature flow equation has been studied intensely by...
New results on quantum tunneling between deep potential wells,
in the presence of a strong constant magnetic field are presented.
This includes a family of double well potentials containing
examples for which the low-energy eigenvalue splitting...
We consider an energy model for N ordered elastic membranes
subject to forcing and boundary conditions. The heights of the
membranes are described by real functions u_1, u_2,...,u_N, which
minimize an energy functional involving the Dirichlet...
We study multiply warped product geometries
MN:=Bn×Fn1×···×FnA
g = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an
open set of initial data within multiply warped product geometries
the Ricci flow starting at any of those develops...
I will describe some new "coarse-graining" methods in
quantitative homogenization and how they can be used to give
rigorous versions of certain heuristic "renormalization group"
arguments in physics, with a focus on several examples.
A fractal uncertainty principle (FUP) roughly says that
a
function and its Fourier transform cannot both be concentrated on
a
fractal set. These were introduced to harmonic analysis in order
to
prove new results in quantum chaos: if eigenfunctions...
