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Persistent Manifolds are Normally Hyperbolic [PDF]

Transactions of the American Mathematical Society, 1978
Let M be a smooth manifold, f : M ∣ a C 1 f:\,M\,\mid \text {a}\,{{C}^{1}} diffeomorphism and V ⊂ M a
Ricardo Mañé
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A Characterization of Hyperbolic Manifolds [PDF]

Proceedings of the American Mathematical Society, 1993
In this note we prove that a complex manifold X X is Kobayashi hyperbolic if and only if the space Hol ⁡ ( Δ , X ) \operatorname {Hol} (\Delta ,X) of holomorphic maps of the unit disk Δ \Delta into X X is relatively compact (with ...
Marco Abate
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An example of an almost hyperbolic Hermitian manifold [PDF]

International Journal of Mathematics and Mathematical Sciences, 1998
The almost hyperbolic Hermitan manifolds introduced in [1] were classified for the first time in [2]. In this note we construct an example of an almost hyperbolic Hermitan manifold which belongs to a certain class that we study here.
Cornelia-Livia Bejan, Liviu Ornea
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A note on homogeneous hyperbolic manifolds [PDF]

Kyoto Journal of Mathematics, 1984
It is proved that a hyperbolic manifold admitting a transitive action of a solvable Lie group is isomorphic to a bounded homogeneous domain in \({\mathbb{C}}^ n.\) Recently the author generalized this result to an arbitrary transitive Lie group action [the author: ''Homogeneous hyperbolic manifolds and homogeneous Siegel domains'', preprint.] Therefore
Kazufumi Nakajima
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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
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The spectrum of an asymptotically hyperbolic Einstein manifold [PDF]

, 1994
This paper relates the spectrum of the scalar Laplacian of an asymptotically hyperbolic Einstein metric to the conformal geometry of its ``ideal boundary'' at infinity. It follows from work of R. Mazzeo that the essential spectrum of such a metric on an $
John M. Lee
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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
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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
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On the automorphism groups of hyperbolic manifolds [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2001
We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension $n\ne 3$, whose group of holomorphic automorphisms has dimension $n^2+1$ and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel space.
Alexander Isaev, Steven G. Krantz
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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
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