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A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE
Part of
- Global differential geometry
Clément Debin
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 2 / March 2020

Published online by Cambridge University Press:

10 April 2018, pp. 597-645

Print publication:

March 2020
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We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.

Intersection K-theory for isolated conical singularities
André Legrand, David Poutriquet
Journal:

Journal of K-Theory / Volume 9 / Issue 1 / February 2012

Published online by Cambridge University Press:

18 February 2011, pp. 177-200

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February 2012
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Starting from the Karoubi multiplicative K-theory, we construct a Chern-Weil theory adapted to isolated conical singularities. The Chern character takes its values in the intersection cohomology of Goresky-MacPherson. We also propose an integer intersection K-theory for such singularities.

DIFFRACTIVE GEODESICS OF A POLYGONAL BILLIARD
Luc Hillairet
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 1 / February 2006

Published online by Cambridge University Press:

02 February 2006, pp. 71-86
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We define the notion of diffractive geodesic for a polygonal billiard or, more generally, for a Euclidean surface with conical singularities. We study the local geometry of the set of such geodesics of given length and we relate it to a number that we call classical complexity. This classical complexity is then computed for any diffractive geodesic. As an application we describe the set of periodic diffractive geodesics as well as the symplectic aspects of the ‘diffracted flow’.

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3 results

A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE

Intersection K-theory for isolated conical singularities

DIFFRACTIVE GEODESICS OF A POLYGONAL BILLIARD