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On index formulas for manifolds with metric horns

Lesch, M.; Peyerimhoff, N.


M. Lesch


In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauss-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have unique closed extensions. But there always exist two extremal extensions D_min and D_max. We describe the quotient of their domains explicitely in geometric resp. topological terms of the base manifolds of the metric horns. We derive index formulas for the Spin-Dirac and Gauss-Bonnet operator. For the Signature operator we present a partial result.


Lesch, M., & Peyerimhoff, N. (1998). On index formulas for manifolds with metric horns. Communications in Partial Differential Equations, 23(3 & 4), 649-684

Journal Article Type Article
Publication Date 1998
Journal Communications in Partial Differential Equations
Print ISSN 0360-5302
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 23
Issue 3 & 4
Pages 649-684