Related papers: Classification of compact real surfaces: a quick p…
We use the techniques of birational algebraic geometry and some combinatorial arguments related to weighted trees to study the structure of resolutions of compactifications of hypothetical counterexamples to the two-dimensional Jacobian…
A brief proof of Lie's classification of solvable algebras of vector fields on the plane is given. The proof uses basic representation theory and PDEs.
We document some versions, in real K-theory, of well-known properties of the coarse assembly map in complex K-theory. These results are well-known, but difficult to find in the literature.
We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth,…
The purpose of this paper is to provide a proof of James' weak compactness theorem that is able to be taught in a first year graduate class in functional analysis.
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex…
The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of…
It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.
Real algebraic geometry provides certificates for the positivity of polynomials on semi-algebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalitites. We show how Putinar's theorem for…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We show the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a quotient manifold of $\mathbb{S}^{n-1}\times \mathbb{R}$…
In this note we give a detailed proof of certain results on geometry of numbers in the $S$-adic case. These results are well-known to experts, so the aim here is to provide a convenient reference for the people who need to use them.
We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not…
In this note, we construct some minimal smooth surfaces of general type with canonical map of degree $ 13, 15, 17, 18, 21, 22 $. These surfaces are constructed as $ \mathbb{Z}_{3}^2$-covers of a blow-up of $ \mathbb{P}^1 \times \mathbb{P}^1…
We classify minimal pairs (X, G) for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X^G and the quotient surface Y = X/G as well as the fundamental group of the smooth part…
This article is a comprised version of my doctoral thesis defended at Basel University in 1995. It concerns circle packings on compact surfaces of any genus.
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
We classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces and they are all arithmetic, i.e., they are…