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A natural smooth compactiffcation of the space of elliptic curves in projective space via blowing up the space of stable maps
projective space stable maps
2015/7/14
We nd it interesting that such a natural naive approach as we will describe
actually works, and yields a desingularization with these nice properties.
Competitively Coupled Maps and Spatial Pattern Formation
Competitively Coupled Maps Spatial Pattern Formation
2012/4/26
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially h...
Stability of Stationary Wave Maps from a Curved Background to a Sphere
Stability of Stationary Wave Maps Curved Background Sphere
2012/4/18
We study time and space equivariant wave maps from $M\times\RR\rightarrow S^2,$ where $M$ is diffeomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metri...
Holder continuity and injectivity of optimal maps
Holder continuity injectivity of optimal maps Analysis of PDEs Differential Geometry
2011/8/25
Abstract: Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c...
Conditional global regularity of Schroedinger maps: sub-threshold dispersed energy
Conditional global regularity Schroedinger maps sub-threshold dispersed energy
2011/2/22
We consider the Schr¨odinger map initial value problem ( ∂tϕ = ϕ × ϕ ϕ(x, 0) = ϕ0(x),
with ϕ0 : R2 ! S2 ֒! R3 a smooth H1 Q map from the Euclidean space R2 ...
Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/20
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and
v denotes the matrix mu...
Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions
equivariant Schroedinger Maps two spatial dimensions
2010/12/1
We consider the Schr¨odinger Map equation in 2 + 1 dimensions, with values into S2. This admits a lowest energy steady state Q, namely the stereographic projection,which extends to a two dimensional f...