Smooth Random Surfaces from Tight Immersions?

TL;DR

This paper explores different mathematical actions for modeling random surfaces, comparing their behaviors to understand which best captures the properties of smooth, randomly curved surfaces.

Contribution

It introduces and compares new actions involving gaussian, extrinsic curvature, and Steiner terms for dynamically triangulated random surfaces.

Findings

Different actions produce distinct surface behaviors.

The modulus of gaussian curvature influences surface smoothness.

Comparative analysis highlights the most effective models.

Abstract

We investigate actions for dynamically triangulated random surfaces that consist of a gaussian or area term plus the {\it modulus} of the gaussian curvature and compare their behavior with both gaussian plus extrinsic curvature and ``Steiner'' actions.