2011, 2011(Special): 568-577. doi: 10.3934/proc.2011.2011.568

A natural differential operator on conic spaces

1. 

Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany

Received  July 2010 Revised  January 2011 Published  October 2011

We introduce the notion of a conic space, as a natural structure on a manifold with boundary, and de ne a natural fi rst order di fferential operator, $c_d_\partial$, acting on boundary values of conic one-forms. Conic structures arise, for example, from resolutions of manifolds with conic singularities, embedded in a smooth ambient space. We show that pull-backs of smooth ambient one-forms to the resolution are cd@-closed, and that this is the only local condition on oneforms that is invariantly de ned on conic spaces. The operator $c_d_\partial$ extends to conic Riemannian metrics, and $c_d_\partial$-closed conic metrics have important geometric properties like the existence of an exponential map at the boundary.
Citation: Daniel Grieser. A natural differential operator on conic spaces. Conference Publications, 2011, 2011 (Special) : 568-577. doi: 10.3934/proc.2011.2011.568
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