We describe the construction of theta summable and finitely summable spectral
triples associated to Mumford curves and some classes of higher dimensional
buildings. The finitely summable case is constructed by considering the
stabilization of the algebra of the dual graph of the special fiber of the
Mumford curve and a variant of the Antonescu-Christensen spectral geometries
for AF algebras. The information on the Schottky uniformization is encoded in
the spectral geometry through the Patterson-Sullivan measure on the limit set.
Some higher rank cases are obtained by adapting the construction for trees.Comment: 23 pages, LaTeX, 2 eps figures, contributed to a proceedings volum
