Computing minimal surfaces with differential forms

Computing Discrete Minimal Surfaces and Their Conjugates

We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of Þxed or free boundary curves in R, S and H. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem fo...

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Computing Parameterizations of Triangulated Surfaces with minimal metric Deformation

Computing isogeny covariant differential modular forms

We present the computation modulo p2 and explicit formulas for the unique isogeny covariant differential modular form of order one and weight χ−p−1,−p called fjet, an isogeny covariant differential modular form of order two and weight χ−p2−p,−1,−1 denoted by fjethjet, and an isogeny covariant differential modular form hjet of order two and weight χ1−p2,0,−1.

Tubular Surfaces Extraction with Minimal Action Surfaces

This paper presents a new fast approach for surfaces extraction of tubular structures, such as blood vessels, tracheas, and colons. Since they are usually long and thin, when being extracted with the traditional Minimal Action Surface method, edges leakage problem could not be avoided. So a front freezing criterion based on the front's average energy is developed. To freeze the tail of the fron...