We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot a...

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a bou...

In the large-N limit of d = 4, N = 4 gauge theory, the dual AdS space becomes flat. We identify a gauge theory correlator whose largeN limit is the flat space S-matrix.

We try to understand the relationship between the K(π, 1)-property of the complexified regular orbit space of a finite reflection group and the flat structure on the orbit space via the uniformization equation attached to the flat structure.

By using logarithm of derivation, logarithm of a differential form is defined. It allows to define fractional order differential forms on a flat space. Regularized volume form on a flat infinite-dimensional space is defined by using fractional order differential forms. Applying noncommutative connection, we show regularized volume form can be defined on a mapping space, if its string class vani...