Geometry

1801 Submissions

[7] viXra:1801.0347 [pdf] replaced on 2018-01-27 07:26:09

The Flow of Ricci-Schrödinger

Authors: Antoine Balan
Comments: 2 pages, written in french

The flow of Ricci-Schrödinger is defined from the Ricci flow, like the Schrödinger equation with respect to the heat equation.
Category: Geometry

[6] viXra:1801.0309 [pdf] submitted on 2018-01-23 19:52:26

Remarks on Liouville-Type Theorems on Complete Noncompact Finsler Manifolds

Authors: Songting Yin, Pan Zhang
Comments: 9 Pages.

In this paper, we give a gradient estimate of positive solution to the equation $$\Delta u=-\lambda^2u, \ \ \lambda\geq 0$$ on a complete non-compact Finsler manifold. Then we obtain the corresponding Liouville-type theorem and Harnack inequality for the solution. Moreover, on a complete non-compact Finsler manifold we also prove a Liouville-type theorem for a $C^2$-nonegative function $f$ satisfying $$\Delta f\geq cf^d, c>0, d>1, $$ which improves a result obtained by Yin and He.
Category: Geometry

[5] viXra:1801.0292 [pdf] submitted on 2018-01-22 15:19:04

An Upper Bound for Lebesgue’s Universal Covering Problem

Authors: Philip Gibbs
Comments: 21 Pages.

The universal covering problem as posed by Henri Lebesgue in 1914 seeks to find the convex planar shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclidean plane. Methods used previously to construct such a cover can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.
Category: Geometry

[4] viXra:1801.0156 [pdf] submitted on 2018-01-13 21:02:25

A Remark on the Localization Formulas About Two Killing Vector Fields

Authors: Xu Chen
Comments: 13 Pages.

In this article, we will discuss a localization formulas of equlvariant cohomology about two Killing vector fields on the set of zero points ${\rm{Zero}}(X_{M}-\sqrt{-1}Y_{M})=\{x\in M \mid |Y_{M}(x)|=|X_{M}(x)|=0 \}.$ As application, we use it to get formulas about characteristic numbers and to get a Duistermaat-Heckman type formula on symplectic manifold.
Category: Geometry

[3] viXra:1801.0155 [pdf] submitted on 2018-01-13 21:07:54

A Poincaré-Hopf Type Formula for A Pair of Vector Fields

Authors: Xu Chen
Comments: 7 Pages.

We extend the reslut about Poincar\'e-Hopf type formula for the difference of the Chern character numbers (cf.[3]) to the non-isolated singularities, and establish a Poincar\'e-Hopf type formula for a pair of vector field with the function $h^{T_{\mathbb{C}}M}(\cdot,\cdot)$ has non-isolated zero points over a closed, oriented smooth manifold of dimension $2n$.
Category: Geometry

[2] viXra:1801.0146 [pdf] submitted on 2018-01-13 01:53:56

Sennimalai Kalimuthu Publications

Authors: Sennimalai Kalimuthu
Comments: 03 Pages. Interested people may contact k,me at any time. Tha

The 5th Euclidean postulate is 2300 years old mathematical impossibility. I have worked on this problem for nearly b35 years and found a number of consistent solutions. My findings have been appeared in international peer reviewed research journals. Generation of power freely from space, space Bombs, Lion’s Tonic and Lemurian Yoga are my ambitious scientific projects. Interested researchers and people may contact me at +91 8508991577. My email is math.kalimuthu@gmail.com and arutperunjothi@outlook.com
Category: Geometry

[1] viXra:1801.0056 [pdf] submitted on 2018-01-05 09:56:59

Poliedros Fórmulas Indemostradas

Authors: Carlos Alejandro Chiappini
Comments: 7 Pages.

Leonhard Euler demostró que en un poliedro regular convexo hay tres números ue cumplen una ley, expresada en una ecuación conocida como fórmula de Euler. Son el número de caras, el número de vértices y el número de aristas. Este documento presenta algunas fórmulas más, obtenidas por ensayo y error a partir de una tabla que contiene los datos de los 5 poliedros regulares convexos. Estas fórmulas indemostradas tienen rasgos verosímiles. Buscar el modo de demostrar la invalidez o la validez de esas fórmulas podría ser, para las personas amantes de la topología, una tarea interesante.
Category: Geometry