The Category of Differential Triads
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and well-posedness (Levi condition).
The Cauchy problem with logarithmic ramifications for -modules
The chess conjecture.
The closure of the space of homeomorphisms on a manifold. The piecewise linear case
The cohomology of with integer coefficients
The cohomology of holomorphic self maps of the Riemann sphere.
The cohomology solution and the index theorem on ring surfaces of genus .
The cokernel of the operator acting on a -module, II
The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.
The compositions of differential operations and the Gâteaux directional derivative.
The computation of the index of a Morse function at a critical point.
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The configuration space integral for links in .
The configuration space of gauge theory on open manifolds of bounded geometry
We define suitable Sobolev topologies on the space of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.
The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces.
The Conley index in Hilbert spaces and its applications
We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having...
The Conley index over a space.