Related papers: Some new theorems in plane geometry

We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.

The purpose of this thesis is to use the language of orbifold groupoids to describe the geometry and topology of orbifolds, highlighting advantages and disadvantages of this language as they arise.

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…

The aim of this paper is to give new representation theorems for extended contact algebras. These representation theorems are based on equivalence relations.

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

In this paper, we study a point-hyper plane incidence theorem in matrix rings, which generalizes all previous works in literature of this direction.

In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.

This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…

We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given…

We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.

In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.

The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…

We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.

This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…

This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…