Hyperbolic manifold
View article: Projection kernels for parameter-dependent hyperbolic operators on globally hyperbolic Lorentzian manifolds
Projection kernels for parameter-dependent hyperbolic operators on globally hyperbolic Lorentzian manifolds Open
This work develops the microlocal and operator-theoretic backbone of a broad class of projection-based approaches to quantum theory and field theory on curved spacetime. It studies “causal projection kernels” that map states on a compact i…
View article: Projection kernels for parameter-dependent hyperbolic operators on globally hyperbolic Lorentzian manifolds
Projection kernels for parameter-dependent hyperbolic operators on globally hyperbolic Lorentzian manifolds Open
This work develops the microlocal and operator-theoretic backbone of a broad class of projection-based approaches to quantum theory and field theory on curved spacetime. It studies “causal projection kernels” that map states on a compact i…
View article: (E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann Hypothesis
(E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann Hypothesis Open
DOI: 10.5281/zenodo.17909003Title: (E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann HypothesisAuthor: Miles Enoch Tracy contact: [email protected] ORCID: https://orci…
View article: (E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann Hypothesis
(E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann Hypothesis Open
DOI: 10.5281/zenodo.17909003Title: (E→S→D→C), Geometric Quantization via Hyperbolic Unfolding: An Arithmetic Impedance Matching Framework for the Riemann HypothesisAuthor: Miles Enoch Tracy contact: [email protected] ORCID: https://orci…
View article: Equiaffine immersions and pseudo-Riemannian space forms
Equiaffine immersions and pseudo-Riemannian space forms Open
We introduce an explicit construction that produces immersions into the pseudosphere $\mathbb{S}^{n,n+1}$ and the pseudohyperbolic space $\mathbb{H}^{n+1,n}$ starting from equiaffine immersions in $\mathbb{R}^{n+1}$, and conversely. We des…
View article: Equiaffine immersions and pseudo-Riemannian space forms
Equiaffine immersions and pseudo-Riemannian space forms Open
We introduce an explicit construction that produces immersions into the pseudosphere $\mathbb{S}^{n,n+1}$ and the pseudohyperbolic space $\mathbb{H}^{n+1,n}$ starting from equiaffine immersions in $\mathbb{R}^{n+1}$, and conversely. We des…
View article: Family of hyperbolic manifolds with exponential homology torsion growth
Family of hyperbolic manifolds with exponential homology torsion growth Open
In this note, we construct a family of hyperbolic manifolds with exponentially growing torsion in their homology groups. This demonstrates that the recent bound on homological torsion, established by Bader, Gelander, and Sauer, is asymptot…
View article: Family of hyperbolic manifolds with exponential homology torsion growth
Family of hyperbolic manifolds with exponential homology torsion growth Open
In this note, we construct a family of hyperbolic manifolds with exponentially growing torsion in their homology groups. This demonstrates that the recent bound on homological torsion, established by Bader, Gelander, and Sauer, is asymptot…
View article: Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces
Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces Open
The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact …
View article: Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3 Open
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact …
View article: Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3 Open
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact …
View article: Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces
Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces Open
The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact …
View article: The IFO (Ibaguner Fractal Operator) Hyperbolic Confinement, & the Solutions of the Jacobian Conjecture & the Dedekind Number Problem
The IFO (Ibaguner Fractal Operator) Hyperbolic Confinement, & the Solutions of the Jacobian Conjecture & the Dedekind Number Problem Open
We introduce the Ibaguner Fractal Operator (IFO) model a geometric framework based on confining hyperbolic expansions inside a cylinder r = 1and demonstrate its profound power by solving two of the most stubborn problems in discrete andalg…
View article: The IFO (Ibaguner Fractal Operator) Hyperbolic Confinement, & the Solutions of the Jacobian Conjecture & the Dedekind Number Problem
The IFO (Ibaguner Fractal Operator) Hyperbolic Confinement, & the Solutions of the Jacobian Conjecture & the Dedekind Number Problem Open
We introduce the Ibaguner Fractal Operator (IFO) model a geometric framework based on confining hyperbolic expansions inside a cylinder r = 1and demonstrate its profound power by solving two of the most stubborn problems in discrete andalg…
View article: Modular Picard Theorems on Hyperbolic Riemann Surfaces
Modular Picard Theorems on Hyperbolic Riemann Surfaces Open
This paper explores modular generalizations of Picard's theorems on hyperbolic Riemann surfaces. Classical Picard theorems establish profound results concerning the values taken by entire or meromorphic functions. When the domain or codoma…
View article: Horofunction compactifications and local Gromov model domains
Horofunction compactifications and local Gromov model domains Open
We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under which, given a domain $Ω$ as above, the identity map from …
View article: Free Cores and Amenable Envelopes in Gromov-Hyperbolic Groups
Free Cores and Amenable Envelopes in Gromov-Hyperbolic Groups Open
This paper investigates the intricate interplay between free subgroups and amenable structures within the framework of Gromov-hyperbolic groups. We formally define and characterize "free cores" as maximal non-elementary free subgroups and …
View article: Modular Picard Theorems on Hyperbolic Riemann Surfaces
Modular Picard Theorems on Hyperbolic Riemann Surfaces Open
This paper explores modular generalizations of Picard's theorems on hyperbolic Riemann surfaces. Classical Picard theorems establish profound results concerning the values taken by entire or meromorphic functions. When the domain or codoma…
View article: Free Cores and Amenable Envelopes in Gromov-Hyperbolic Groups
Free Cores and Amenable Envelopes in Gromov-Hyperbolic Groups Open
This paper investigates the intricate interplay between free subgroups and amenable structures within the framework of Gromov-hyperbolic groups. We formally define and characterize "free cores" as maximal non-elementary free subgroups and …
View article: Horofunction compactifications and local Gromov model domains
Horofunction compactifications and local Gromov model domains Open
We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under which, given a domain $Ω$ as above, the identity map from …
View article: Hyperbolic Dehn Surgery and the Volume Conjecture for Knots in 3-Manifolds
Hyperbolic Dehn Surgery and the Volume Conjecture for Knots in 3-Manifolds Open
This paper explores the intricate relationship between hyperbolic Dehn surgery and the Volume Conjecture for knots within 3-manifolds. We investigate how the geometric invariants of hyperbolic 3-manifolds obtained through Dehn surgery on k…
View article: Hyperbolic Dot Products: Geometry-Aware Similarity for Non-Euclidean Embeddings
Hyperbolic Dot Products: Geometry-Aware Similarity for Non-Euclidean Embeddings Open
The ubiquitous Euclidean dot product serves as a fundamental measure of similarity in numerous machine learning applications, ranging from recommender systems to natural language processing. However, an increasing volume of complex, hierar…
View article: Hyperbolic Dehn Surgery and the Volume Conjecture for Knots in 3-Manifolds
Hyperbolic Dehn Surgery and the Volume Conjecture for Knots in 3-Manifolds Open
This paper explores the intricate relationship between hyperbolic Dehn surgery and the Volume Conjecture for knots within 3-manifolds. We investigate how the geometric invariants of hyperbolic 3-manifolds obtained through Dehn surgery on k…
View article: Hyperbolic Cone Manifolds and the Volume Conjecture for Knots
Hyperbolic Cone Manifolds and the Volume Conjecture for Knots Open
This paper explores the deep connection between hyperbolic geometry and knot theory, focusing on hyperbolic cone manifolds obtained by coning along knots, and their relation to the Volume Conjecture. We investigate the geometric properties…
View article: The Amenable-Free Dichotomy in Gromov Hyperbolic Groups: A Geometric Characterization
The Amenable-Free Dichotomy in Gromov Hyperbolic Groups: A Geometric Characterization Open
This paper rigorously investigates the amenable-free dichotomy within the class of Gromov hyperbolic groups, focusing on establishing a comprehensive geometric characterization. Gromov hyperbolic groups exhibit rich geometric properties, m…
View article: The Amenable-Free Dichotomy in Gromov Hyperbolic Groups: A Geometric Characterization
The Amenable-Free Dichotomy in Gromov Hyperbolic Groups: A Geometric Characterization Open
This paper rigorously investigates the amenable-free dichotomy within the class of Gromov hyperbolic groups, focusing on establishing a comprehensive geometric characterization. Gromov hyperbolic groups exhibit rich geometric properties, m…
View article: Gromov Hyperbolicity: The Canonical Setting for the Free-Amenable Dichotomy
Gromov Hyperbolicity: The Canonical Setting for the Free-Amenable Dichotomy Open
This paper explores the profound connection between Gromov hyperbolicity and the fundamental free-amenable dichotomy in group theory. We argue that Gromov hyperbolic spaces and groups provide a canonical geometric framework where this dich…
View article: Hyperbolic Cone Manifolds and the Volume Conjecture for Knots
Hyperbolic Cone Manifolds and the Volume Conjecture for Knots Open
This paper explores the deep connection between hyperbolic geometry and knot theory, focusing on hyperbolic cone manifolds obtained by coning along knots, and their relation to the Volume Conjecture. We investigate the geometric properties…
View article: Gromov Hyperbolicity: The Canonical Setting for the Free-Amenable Dichotomy
Gromov Hyperbolicity: The Canonical Setting for the Free-Amenable Dichotomy Open
This paper explores the profound connection between Gromov hyperbolicity and the fundamental free-amenable dichotomy in group theory. We argue that Gromov hyperbolic spaces and groups provide a canonical geometric framework where this dich…
View article: Amenable Actions and the Margulis Quotient Conjecture for Hyperbolic Groups
Amenable Actions and the Margulis Quotient Conjecture for Hyperbolic Groups Open
This paper explores the interplay between amenable group actions and the Margulis Quotient Conjecture within the context of hyperbolic groups. We investigate how the existence of amenable actions with specific properties influences the str…