Results 1  10
of
159,509
Filling Riemannian manifolds
 J. of Differential Geometry
, 1983
"... We want to discuss here several unsolved problems concerning metric invariants of a Riemannian manifold V = (V, g) which mediate between the curvature and topology of V. ..."
Abstract

Cited by 325 (6 self)
 Add to MetaCart
We want to discuss here several unsolved problems concerning metric invariants of a Riemannian manifold V = (V, g) which mediate between the curvature and topology of V.
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
Abstract

Cited by 454 (2 self)
 Add to MetaCart
This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
 Advances in Neural Information Processing Systems 14
, 2001
"... Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
Abstract

Cited by 664 (8 self)
 Add to MetaCart
Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
Abstract

Cited by 453 (17 self)
 Add to MetaCart
This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
 BULL. AMER. MATH. SOC
, 1982
"... ..."
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
Abstract

Cited by 529 (3 self)
 Add to MetaCart
Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
Abstract

Cited by 775 (31 self)
 Add to MetaCart
There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract

Cited by 543 (11 self)
 Add to MetaCart
to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings
A Tutorial on Visual Servo Control
 IEEE Transactions on Robotics and Automation
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
Abstract

Cited by 822 (25 self)
 Add to MetaCart
review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any
Results 1  10
of
159,509