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Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (60 self)
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, which resemble HamiltonJacobi equations with parabolic righthand sides, by using techniques from hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps
Real hyperbolic on the outside, complex hyperbolic on the inside
 Inv. Math
"... The rank one symmetric spaces of negative curvature come in three infinite families: real hyperbolic space Hn; complex hyperbolic space CHn; and quaternionic hyperbolic space QHn. (The Cayley plane is the remaining example.) Aside from the obvious embeddings Hn ↪ → CHn ↪ → QHn ..."
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Cited by 14 (0 self)
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The rank one symmetric spaces of negative curvature come in three infinite families: real hyperbolic space Hn; complex hyperbolic space CHn; and quaternionic hyperbolic space QHn. (The Cayley plane is the remaining example.) Aside from the obvious embeddings Hn ↪ → CHn ↪ → QHn
A Focus+Context Technique Based on Hyperbolic Geometry for Visualizing Large Hierarchies
 SIGCHI CONFERENCE ON HUMAN FACTORS IN COMPUTING SYSTEMS (CHI '95)
, 1995
"... We present a new focus+context (fisheye) technique for visualizing and manipulating large hierarchies. Our technique assigns more display space to a portion of the hierarchy while still embedding it in the context of the entire hierarchy. The essence of this scheme is to lay out the hierarchy in a ..."
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Cited by 411 (1 self)
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We present a new focus+context (fisheye) technique for visualizing and manipulating large hierarchies. Our technique assigns more display space to a portion of the hierarchy while still embedding it in the context of the entire hierarchy. The essence of this scheme is to lay out the hierarchy in a
M.Noguchi ,The heat kernel on hyperbolic space
 Bull.London Math.Soc
, 1998
"... 1 Introduction and the main result The purpose of this note is to provide a new proof for the explicit formulas of the heat kernel on hyperbolic space. By definition, the hyperbolic space Hn is a (unique) simply connected complete ndimensional Riemannian manifold with a constant negative sectional ..."
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Cited by 16 (0 self)
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1 Introduction and the main result The purpose of this note is to provide a new proof for the explicit formulas of the heat kernel on hyperbolic space. By definition, the hyperbolic space Hn is a (unique) simply connected complete ndimensional Riemannian manifold with a constant negative sectional
Nonscaleinvariant inverse curvature flows in hyperbolic space
, 2012
"... Abstract. We consider inverse curvature flows in hyperbolic space Hn+1 with starshaped initial hypersurface, driven by positive powers of a homogeneous curvature function. The solutions exist for all time and, after rescaling, converge to a sphere. Contents ..."
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Cited by 5 (4 self)
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Abstract. We consider inverse curvature flows in hyperbolic space Hn+1 with starshaped initial hypersurface, driven by positive powers of a homogeneous curvature function. The solutions exist for all time and, after rescaling, converge to a sphere. Contents
Existence of constant mean curvature graphs in hyperbolic space
 Calc. Var. Partial Differential Equations
, 1999
"... Abstract. We give an existence result for constant mean curvature graphs in hyperbolic space Hn+1. Let Ω be a compact domain of a horosphere in Hn+1 whose boundary ∂Ω is mean convex, that is, its mean curvature H∂Ω (as a submanifold of the horosphere) is positive with respect to the inner orientatio ..."
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Cited by 9 (3 self)
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Abstract. We give an existence result for constant mean curvature graphs in hyperbolic space Hn+1. Let Ω be a compact domain of a horosphere in Hn+1 whose boundary ∂Ω is mean convex, that is, its mean curvature H∂Ω (as a submanifold of the horosphere) is positive with respect to the inner
The Delaunay tessellation in hyperbolic space
, 2013
"... Abstract. The Delaunay tessellation of a locally finite subset of the hyperbolic space Hn is constructed via convex hulls in Rn+1. Basic properties, including the empty circumspheres condition and geometric duality with the Voronoi tessellation, are proved and compared with those of the Euclidean ve ..."
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Cited by 1 (1 self)
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Abstract. The Delaunay tessellation of a locally finite subset of the hyperbolic space Hn is constructed via convex hulls in Rn+1. Basic properties, including the empty circumspheres condition and geometric duality with the Voronoi tessellation, are proved and compared with those of the Euclidean
COMPLETE SUBMANIFOLDS IN A HYPERBOLIC SPACE
"... Abstract. In this paper, we study ndimensional (n ≥ 3) complete submanifolds Mn in a hyperbolic space Hn+p(−1) with the scalar curvature n(n − 1)R and the mean curvature H being linearly related. Suppose that the normalized mean curvature vector field is parallel and the mean curvature is positive ..."
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Abstract. In this paper, we study ndimensional (n ≥ 3) complete submanifolds Mn in a hyperbolic space Hn+p(−1) with the scalar curvature n(n − 1)R and the mean curvature H being linearly related. Suppose that the normalized mean curvature vector field is parallel and the mean curvature
RADIAL FAST DIFFUSION ON THE HYPERBOLIC SPACE
"... Abstract. We consider positive radial solutions to the fast diffusion equation ut = ∆(um) on the hyperbolic space HN for N ≥ 2, m ∈ (ms, 1), ms = N−2N+2. By radial we mean solutions depending only on the geodesic distance r from a given point o ∈ HN. We investigate their fine asymptotics near the ex ..."
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Abstract. We consider positive radial solutions to the fast diffusion equation ut = ∆(um) on the hyperbolic space HN for N ≥ 2, m ∈ (ms, 1), ms = N−2N+2. By radial we mean solutions depending only on the geodesic distance r from a given point o ∈ HN. We investigate their fine asymptotics near
STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY
, 1997
"... This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the ..."
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Cited by 260 (14 self)
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This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors
Results 1  10
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4,388