Related papers: Embedded minimal disks

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…

This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portoro\v{z} on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of…

This paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. In [CM3]-[CM5] we describe the case where the surfaces are topologically disks on…

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic…

The magnetic hard disc drive industry continues to face serious challenges in its quest for ever decreasing bit size. This review summarizes recent advances and promising new technology which have foundations in fundamental physical…

This is a short and rather narrative summary of our ongoing efforts in identifying white dwarfs with gaseous debris disks, and developing an understanding of the structure and origin of these disks.

We determine the excluded minors characterising the class of countable graphs that embed into some compact surface.

In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.

Spin qubits have emerged as a leading platform for quantum information processing due to their long coherence times, small footprint, and compatibility with the existing semiconductor industry. We first provide an introduction to the…

Due to the recent renewal in the interest for embedded surfaces we provide a list of commented references of interest.

For any prescribed closed subset of a line segment in Euclidean 3-space, we construct a sequence of minimal disks that are properly embedded in an open solid cylinder around the segment and that have curvatures blowing up precisely at the…

Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…

In this work we prove the existence of embedded closed minimal hypersurfaces in non-compact manifolds containing a bounded open subset with smooth and strictly mean-concave boundary and a natural behavior on the geometry at infinity. For…

We review the literature on trainable, compressed embedding layers and discuss their applicability for compressing gigantic neural recommender systems. We also report the results we measured with our compressed embedding layers.

We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh,…

In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were…

We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have…

We construct three kinds of complete embedded minimal surfaces in $\Bbb H^2\times \Bbb R$. The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These…

For any m > 0, we construct properly embedded minimal surfaces in H^2 x R with genus zero, infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable number of limit ends. All these examples…

In this paper, we prove that every confomal minimal immersion of an open Riemann surface into $\mathbb{R}^n$ for $n\ge 5$ can be approximated uniformly on compacts by conformal minimal embeddings. Furthermore, we show that every open…