相关论文: On the Theorem of the Three Perpendiculars

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.

In this paper we prove a rigidity result for the equality case of the Penrose inequality on $3$-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality…

In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…

It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…

A curve $\gamma$ in a Riemannian manifold $M$ is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically. In particular, when $\gamma$ lies on an oriented…

We extend Raimi's classical partition theorem to the continuous setting of the circle and $n$-dimensional torus. Building on recent work of Hegyv\'ari, Pach, and Pham in finite groups, we prove that there exist measurable partitions of the…

We show that the hyperplane conjecture holds for the classes of $k$-intersection bodies with arbitrary measures in place of volume.

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.

We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local…

In this paper we prove an infinitesimal version of the classical Terracini Lemma for 3--secant planes to a variety. Precisely we prove that if $X\subseteq \PP^r$ is an irreducible, non--degenerate, projective complex variety of dimension…

We prove the analogue of Johannson's Deformation Theorem for PD3 pairs.

After a review of the results in arXiv:1203.3184 [math-ph] about Pythagorean inequalities for products of spectral triples, I will present some new results and discuss classes of spectral triples and states for which equality holds.

The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a self mapping on PN spaces by means of measure of discontinuity.

We establish a half-space theorem \`a la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.