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Homotopy hyperbolic 3-manifolds are hyperbolic [PDF]

Annals of Mathematics, 2003
This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for
Gabai, David, Meyerhoff, G. Robert, Thurston, Nathaniel   +2 more
core   +6 more sources

Adaptive data embedding for curved spaces [PDF]

iScience
Summary: Recent studies have demonstrated the significance of hyperbolic geometry in uncovering low-dimensional structure within complex hierarchical systems.
Anoop Praturu, Tatyana O. Sharpee
doaj   +2 more sources

Mass rigidity for hyperbolic manifolds [PDF]

Communications in Mathematical Physics, 2019
We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space.
Huang, Lan-Hsuan, Jang, Hyun Chul, Martin, Daniel   +2 more
core   +3 more sources

Hyperbolic Spatial Covariance Modeling with Adaptive Signal Filtering for Robust Wi-Fi Indoor Positioning [PDF]

Sensors
Robust indoor positioning, crucial to modern location-based services, increasingly leverages Channel State Information (CSI) for its superior multipath resolution over the traditional RSSI.
Wenxu Wang, Mingxiang Liu
doaj   +2 more sources

Rootlets Hierarchical Principal Component Analysis for Revealing Nested Dependencies in Hierarchical Data [PDF]

Mathematics
Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level.
Korey P. Wylie, Jason R. Tregellas
doaj   +2 more sources

HC-SPA: Hyperbolic Cosine-Based Symplectic Phase Alignment for Fusion Optimization [PDF]

Sensors
In multimodal collaborative learning, the gradient dynamics of heterogeneous modalities face significant challenges due to the curvature heterogeneity of parameter manifolds and mismatches in phase evolution.
Wenlong Zhang, Aiqing Fang, Ying Li, Yan Wei   +3 more
doaj   +2 more sources

Modeling Tree-like Heterophily on Symmetric Matrix Manifolds [PDF]

Entropy
Tree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein–protein interaction networks.
Yang Wu, Liang Hu, Juncheng Hu
doaj   +2 more sources

Hyperbolic Ricci-Bourguignon-Harmonic Flow [PDF]

Mathematics Interdisciplinary Research, 2022
In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold M coupled with the harmonic map flow between M and a fixed manifold N. At the first, we prove the unique short-time existence to solution of this system.
Shahrood Azami
doaj   +1 more source

Embedding closed hyperbolic 3–manifolds in small volume hyperbolic 4–manifolds [PDF]

Algebraic & Geometric Topology, 2021
In this paper we study existence and lack thereof of closed embedded orientable co-dimension one totally geodesic submanifolds of minimal volume cusped orientable hyperbolic manifolds.
Chu, Michelle, Reid, Alan W.
openaire   +3 more sources

Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures [PDF]

Épijournal de Géométrie Algébrique, 2023
In this paper, we study various hyperbolicity properties for a quasi-compact K\"ahler manifold $U$ which admits a complex polarized variation of Hodge structures so that each fiber of the period map is zero-dimensional.
Ya Deng
doaj   +1 more source