Lowest uniformizations of compact Klein surfaces

Surfaces with Boundary: Their Uniformizations, Determinants of Laplacians, and Isospectrality

Let Σ be a compact surface of type (g, n), n > 0, obtained by removing n disjoint disks from a closed surface of genus g. Assuming χ(Σ) < 0, we show that on Σ, the set of flat metrics which have the same Laplacian spectrum of Dirichlet boundary condition is compact in the C∞ topology. This isospectral compactness extends the result of Osgood, Phillips, and Sarnak [O-P-S3] for type (0, n) surfac...

COVERS OF KLEIN SURFACES by

Compact Klein Surfaces of Genus 5 with a Unique Extremal Disc

A compact (orientable or non-orientable) surface of genus g is said to be extremal if it contains an extremal disc, that is, a disc of the largest radius determined only by g. The present paper concerns non-orientable extremal surfaces of genus 5. We represent the surfaces as side-pairing patterns of a hyperbolic regular 24-gon, that is, a generic fundamental region of an NEC group uniformizing...

Dynamics of Dianalytic Transformations of Klein Surfaces

This paper is an introduction to dynamics of dianalytic self-maps of nonorientable Klein surfaces. The main theorem asserts that dianalytic dynamics on Klein surfaces can be canonically reduced to dynamics of some classes of analytic self-maps on their orientable double covers. A complete list of those maps is given in the case where the respective Klein surfaces are the real projective plane, ...

A Noncommutative Compact Kaluza-klein Cosmology

We study the quantum cosmology of an empty (4+1)-dimensional Kaluza-Klein cosmology with a negative cosmological constant and a RW type metric with two scale factors, one for 4-D universe and the other for one compact extra dimension. By assuming the noncommutativity in the corresponding mini-superspace and Wheeler-DeWitt equation we suggest a solution for the cosmological constant problem. PAC...