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Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
Logarithmic tensor category theory, VI: Expansion condition associativity of logarithmic intertwining operators associativity isomorphisms
2011/2/23
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties
conjugation-free geometric presentation of fundamental groups some properties
2010/12/1
A conjugation-free geometric presentation of a funda-mental group is a presentation with the natural topological gener-ators x1, . . . , xn and the cyclic relations.