Related papers: Minimal submanifolds

Manifold learning is an emerging research domain of machine learning. In this work, we give an introduction into manifold learning and how it is employed for important application fields in multimedia.

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural…

The field of two-dimensional topological semimetals, which emerged at the intersection of two-dimensional materials and topological materials, have been rapidly developing in recent years. In this article, we briefly review the progress in…

We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel…

This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…

This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…

A brief history, the current state, and future directions of spin mechanics are presented.

We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with lambda>=0) in a Euclidean space E^N. Assume that the immersion is proper, that is, the preimage of every compact set in E^N is also…

We discover some very general configuration results for constructing area-minimizing cones. In particular, given any closed minimal submanifold in some Euclidean sphere, every cone over the minimal product of sufficiently many copies of the…

To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…

Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X, in relation with the definability of types.

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

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…

In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.

We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.

In this paper, we introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…