Related papers: The Minimal Genus Problem
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
This article explains a program to study complete and properly embedded minimal surfaces in $\mathbb{R}^3$ developed jointly with W.H. Meeks and A. Ros in the last three decades. It follows closely the structure of my invited ICM talk with…
Ongoing microlensing surveys have already yielded more than five hundred microlensing events, most of which have been identified in real-time. In this review I present the basic theory and observational status of these surveys. I highlight…
We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence…
This is a brief review of the present status, of some recent developments and of the open challenges in string/M theory.
We explore the hypothesis of having an approximate lepton number conservation as a way to achieve a successful leptogenesis in low-scale seesaw mechanisms. The smallness of the active neutrino masses, as well as a strong degeneracy in the…
Few-body research history, achievements, current development and challenges are presented.
This is an extended and pedagogically oriented version of our recent work, in which we proposed an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach.
The new property of minimal surfaces is obtained in this article.
A model of genome evolution is proposed. Based on three assumptions the evolutionary theory of a genome is formulated. The general law on the direction of genome evolution is given. Both the deterministic classical equation and the…
Lawson's iteration is a classical and effective method for solving the linear (polynomial) minimax approximation problem in the complex plane. Extension of Lawson's iteration for the rational minimax approximation problem with both…
Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and…
The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…
This note contains additions to the paper 'Clustered cell decomposition in P-minimal structures' (arXiv:1612.02683). We discuss a question which was raised in that paper, on the order of clustered cells. We also consider a notion of cells…
We study existence of minimisers to the least gradient problem on a strictly convex domain in two settings. On a bounded domain, we allow the boundary data to be discontinuous and prove existence of minimisers in terms of the Hausdorff…
This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
Let $W,W'\subseteq G$ be nonempty subsets in an arbitrary group $G$. The set $W'$ is said to be a complement to $W$ if $WW'=G$ and it is minimal if no proper subset of $W'$ is a complement to $W$. We show that, if $W$ is finite then every…