Related papers: Minimal submanifolds: Encyclopedia of Mathematical…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
New large colliders will probe scales up to few TeV, indicating the way Nature has chosen to extend the Standard Model. We review alternative scenarios to the traditional Minimal Supersymmetric Standard Model: the little Higgs model, split…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
Minimal surfaces and Einstein manifolds are among the most natural structures in differential geometry. Whilst minimal surfaces are well understood, Einstein manifolds remain far less so. This exposition synthesises together a set of…
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
We survey the history as well as recent progress in the Yang problem concerning the existence of complete bounded complex submanifolds of the complex Euclidean spaces. We also point out some open questions on the topic.
An introduction to the physics of heavy fermion compounds is presented, attempting to highlight the conceptual developments and emphasize the mysteries and open questions that persist in this active field of research.
In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.
In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial…
This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…
We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds is a classical subject in…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Supercurrents, as introduced by Lagerberg, were mainly motivated as a way to study tropical varieties. Here we will associate a supercurrent to any smooth submanifold of $\R^n$. Positive supercurrents resemble positive currents in complex…
Examples of nonformal simply connected symplectic manifolds are constructed.
This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in…
Almost-complex and hyper-complex manifolds are considered in this paper from the point of view of complex analysis and potential theory. The idea of holomorphic coordinates on an almost-complex manifold $(M,\mathbf{J}%)$ is suggested by D.…
We present here some classical and modern results about phase transitions and minimal surfaces, which are quite intertwined topics. We start from scratch, revisiting the theory of phase transitions as put forth by Lev Landau. Then, we…