We investigate actions for dynamically triangulated random surfaces that consist of a gaussian or area term plus the modulus of the gaussian curvature and compare their behavior with both gaussian plus extrinsic curvature and “Steiner” actions. Considerable effort has recently been devoted to exploring modifications of the discretized Polyakov partition function [1] for a random surface

In this paper we will prove the Calabi-Yau conjectures for embedded surfaces (i.e., surfaces without self-intersection). In fact, we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations, as will be more apparent once we describe the main steps of the proof later in the introduction. The Calabi-Yau conjectures about surfaces date bac...

The main result of this paper is a homotopy theoretic classification of Legendre immersions from a compact manifold into a contact manifold. The paper also includes normal form theorems for Legendre submanifolds as well as a multi-jet transversality theorem for Legendre

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This paper provides a broad overview of legal and social service responses to child sexual abuse, the overarching legal framework provided by federal legislation, and funding mandates and the unique and shared investigative concerns of law enforcement and child protective service entities. Relevant psychological research is highlighted throughout, including research on investigator training, fo...