Varifolds and generalized curvature
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In this paper, the notions of varifold and generalized mean curvature have been introduced, with a few simple examples, and they have been used to describe a variety of objects.Abstract:
This short note aims at introducing, with a few simple examples, the notions of varifold and generalized mean curvature R esum e Notre objectif est d'aborder les notions de varifold et de courbure gnralise au travers d'exemples simplesread more
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Dissertation
Approximation de surfaces par des varifolds discrets : représentation, courbure, rectifiabilité
TL;DR: In this article, the authors define a forme regularisee de la variation premiere d'un varifold, which permet de definir des energies de Jones approchees which convergent dans l'espace des varifolds vers l'energie de Willmore ainsi qu'une approximation of la courbure which est testee numeriquement dans le Chapitre 6.
Posted Content
Cubical Covers of Sets in $\mathbb{R}^n$
Laramie Paxton,Kevin R. Vixie +1 more
TL;DR: In this paper, the wildest sets for which it is still true that the representations faithfully inform us about the original set is the focus of this rather playful, expository paper that we hope will stimulate interest in cubical coverings as well as other two ideas we explore briefly: Jones' $\beta$ numbers and varifolds from geometric measure theory.
Journal ArticleDOI
Cubical Covers of Sets in R^n
Laramie Paxton,Kevin R. Vixie +1 more
TL;DR: A heuristic, expository approach to estimating the size of various sets and their boundaries, with the goal of preserving important features in the representations.
References
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Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
Book
Functions of Bounded Variation and Free Discontinuity Problems
TL;DR: The Mumford-Shah functional minimiser of free continuity problems as mentioned in this paper is a special function of the Mumfordshah functional and has been shown to be a function of free discontinuity set.
Journal ArticleDOI
On the first variation of a varifold
TL;DR: In this paper, the first variation of the k-dimensional area integral is studied and a regularity theorem for weakly defined k dimensional surfaces in Riemannian manifolds whose first variation is summable to a power greater than k is given.
Book
The motion of a surface by its mean curvature
TL;DR: The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press to preserve the original texts of these important books while presenting them in durable paperback editions.