Related papers: Embedded minimal disks
This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…
This is a survey article on distance-squared mappings and related topics.
We present an informal survey (meant to accompany another paper) on graph compression methods. We focus on lossless methods, briefly list available pproaches, and compare them where possible or give some indicators on their compression…
We survey what is known about minimal surfaces in $\bold R^3 $ that are complete, embedded, and have finite total curvature. The only classically known examples of such surfaces were the plane and the catenoid. The discovery by Costa, early…
This is an introductory article to the theory of multiple gaps.
This paper presents a brief review of our recent work investigating a novel bottom-up approach to realize silicon based nanoelectronics. We discuss fabrication technique, electronic properties and device applications of silicon nanodots as…
In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…
We develop a theory of "minimal $\theta$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is…
In this paper we prove that the \textsc{Min-Bisection} problem is NP-hard on \emph{unit disk graphs}, thus solving a longstanding open question.
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Generalising the two-dimensional case, we provide estimates for the mean-values of the lengths of the edges of an integral box with given volume and minimal surface.
Embedded spaces are a key feature in deep learning. Good embedded spaces represent the data well to support classification and advanced techniques such as open-set recognition, few-short learning and explainability. This paper presents a…
we construct a properly embedded minimal surface in the flat product R^2*S^1 which is quasi-periodic but is not periodic.
Embeddings are ubiquitous in machine learning, appearing in recommender systems, NLP, and many other applications. Researchers and developers often need to explore the properties of a specific embedding, and one way to analyze embeddings is…
We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic metric space whose geometric, topological, and analytic…
Alternative approaches to Lebesgue integration are considered.
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.