Đề tài " Random k-surfaces "

Invariant measures for the geodesic flow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this flow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces. The “2-dimensional” analog of the unit tangent bundle with the geodesic flow is a “space of pointed k-surfaces”, which can be considered as the space of germs of complete k-surfaces passing...