相关论文: Minimal submanifolds
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…
Minimal submanifolds constitute a central area within the realm of differential geometry, due to their many applications in various branches of physics. In this thesis we will employ a recent result of S. Gudmundsson and T.J. Munn to…
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…
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.
We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.
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…
Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more…
In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…
In the present paper, we study harmonic mappings of complete Riemannian manifolds, as well as minimal and stable minimal submanifolds of complete Riemannian manifolds. We examine classical theorems in the theory of these manifolds from 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.
We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.
In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds,…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…
In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.
We provide uniqueness results for compact minimal submanifolds in a large class of Riemannian manifolds of arbitrary dimension. In the case compact and Cartan-Hadamard manifolds we obtain general results for these submanifolds. Several…
We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…
The first papers on o-minimal structures appeared in the mid 1980s, since then the subject has grown into a wide ranging generalisation of semialgebraic, subanalytic and subpfaffian geometry. In these notes we try to show that this is in…