Related papers: Recent Progress on Austere Submanifolds

This is a short, elementary survey article about taut submanifolds. In order to simplify the exposition, we restrict to the case of compact smooth submanifolds of Euclidean or spherical spaces. Some new, partial results concerning taut…

This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.

A review of recent developments in the analyses of supersymmetric dark matter is given.

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

Some recent results in supersymmetric grand unified theories are reviewed.

In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of…

We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of…

After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…

In this survey, we give an introduction to nearly K\"ahler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…

This paper describes some of the ideas used in the development of our work on small gaps between primes.

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.

This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.

The main result of this paper was already obtained in the paper `Some Remarks on the Geometry of Austere Manifolds', by Robert L. Bryant.

We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.

This survey explores a range of classical findings and recent developments related to our understanding of astheno-K\"ahler manifolds. Furthermore, we provide various examples of astheno-K\"ahler manifolds and analyze the challenges…

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…

This paper is a survey on the structure of manifolds with a lower Ricci curvature bound.

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.