Mathematical Proceedings of the Cambridge Philosophical Society

Table of Contents - July 2012 - Volume 153, Issue 01  

Research Article

Isospectral surfaces of genus two and three

DENNIS BARDENa1 and HYUNSUK KANGa2 c1

a1 Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Cambridge CB3 0WB. e-mail: db127@dpmms.cam.ac.uk

a2 Department of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Dong-daemun-gu, Seoul 130-722, Korea. e-mail: h.kang@kias.re.kr

Abstract

We give examples of isospectral non-isometric surfaces of genus two and three with variable curvature, as well as hyperbolic orbifolds of genus two. We apply the first result to construct isospectral potentials on a Riemann surface of genus two.

(Received August 02 2011)

(Revised February 14 2012)

(Online publication February 27 2012)

Correspondence:

c1 Corresponding author