Related papers: Gunther's proof of Nash's isometric embedding theo…
In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
In [The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces. Memoirs of the American Mathematical Society. American Mathematical Society, 2023], Sturm studied the space of all metric measure spaces up…
We present a short and elementary proof of isometric uniqueness of the Gurarii space.
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
Let $(M,g)$ be a $C^\infty$-smooth, $n$-dimensional Riemannian manifold which is diffeomorphic to $\RR^n$ and admit an action of a properly discontinuous and cocompact group. This work proves the existence of a $C^\infty$ equivariant…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach space with a separable dual embeds into one with a shrinking…
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…
With the help of the recently introduced parametric geometry of numbers by W. M. Schmidt and L. Summerer, we prove a strong version of a conjecture of Schmidt concerning the successive minima of a lattice.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
In this article we discuss a generalized Wirtinger inequality.
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We also apply some lemmas to prove the Pizza Theorem.
Royden proved that any isometry of Teichmuller space in the Teichmuller metric must be an element of the extended mapping class group M(S). He also proved that the Teichmuller metric is not symmetric at any point. In this paper we give…
We study finite subsets of $\ell_2$, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional…
We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors.
This is a short note describing what I believe is a serious gap in Stanfield's proof of Sachs' conjecture that every linklessly embeddable graph has a linear linkless embedding in $\mathbb{R}^3$.