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We obtain upper and lower bounds on the heat kernel of a uniformly elliptic operator in divergence form with measurable coefficients. From these bounds one can deduce not only the familiar short‐time asymptotics of the heat kernel, but in the case of periodic coefficients, long‐time asymptotics...
We give a direct proof of an existence theorem for the vortex equations over a compact Riemann surface, exploiting the interpretation of these equations in terms of moment maps.
We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable. Given any integer k > 2, there is no algorithm to determine whether or not any small cancellation...
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