Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

Transonic flow on an axially symmetric torus

AbstractOn a Riemannian manifold the existence (and uniqueness) of subsonic gas flows with prescribed circulation has been previously established (Acta Math. 125 1970, 57–73). If the manifold is a torus of revolution then the gas dynamics equation reduces to a nonlinear ordinary differential equation and the flow can be described explicitly. We show that, as the circulations are increased, one obtains a complete family of solutions: smooth subsonic, smooth transonic, transonic with shocks, and smooth supersonic flows

Continuous families of H-surfaces

SIGLEDEGerman

The extended modular group and sums of squares

Also published in: Proceedings of the workshop on 'Kleinian Groups', Oaxtepec, Mexico, summer 1981SIGLEDEGerman