5 research outputs found
Topological quantum field theory and four-manifolds
I review some recent results on four-manifold invariants which have been
obtained in the context of topological quantum field theory. I focus on three
different aspects: (a) the computation of correlation functions, which give
explicit results for the Donaldson invariants of non-simply connected
manifolds, and for generalizations of these invariants to the gauge group
SU(N); (b) compactifications to lower dimensions, and relations with
three-manifold topology and with intersection theory on the moduli space of
flat connections on Riemann surfaces; (c) four-dimensional theories with
critical behavior, which give some remarkable constraints on Seiberg-Witten
invariants and new results on the geography of four-manifolds.Comment: 10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000;
references adde
Dirichlet boundary conditions for degenerate and singular nonlinear parabolic equations
We study existence and uniqueness of solutions to a class of quasilinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used