Brownian motion parametrized with metric space of constant curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

A Metric of Constant Curvature on Polycycles

We prove the following main theorem of the theory of (r, q)-polycycles. Suppose a nonseparable plane graph satisfies the following two conditions: (1) each internal face is an r-gon, where r ≥ 3 ; (2) the degree of each internal vertex is q , where q ≥ 3 , and the degree of each boundary vertex is at most q and at least 2 . Then it also possesses the following third property: (3) the vertices, ...

Brownian Motion in Minkowski Space

We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem. The first is to define a sequence of stopping times associated with the Brownian “kicks” or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, the Central Limit Theorem (CLT) leads to temperature d...

Hypersurfaces of Constant Curvature in Space Forms

In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Ga...