Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Christopher B. Croke"'
Autor:
Christopher B. Croke, Pilar Herreros
Publikováno v:
Asian Journal of Mathematics. 20:47-58
We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat M\"obius strip are determined by their lens data. We also see by example that the f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cbbd048eb6deff20a58a85a7c3542f83
https://doi.org/10.4310/ajm.2016.v20.n1.a3
https://doi.org/10.4310/ajm.2016.v20.n1.a3
This paper considers metric balls $B(p,R)$ in two dimensional Riemannian manifolds when $R$ is less than half the convexity radius. We prove that $Area(B(p,R)) \geq \frac{8}{\pi}R^2$. This inequality has long been conjectured for $R$ less than half t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be722c2dbde14a8158d27a2382b3b813
Autor:
Christopher B. Croke
Publikováno v:
Bulletin of the London Mathematical Society. 41:701-708
This paper considers Riemannian metrics on two dimensional disks where all geodesics are minimizing. A sharp reverse isoperimetric inequality is proven. This in turn yields near optimal bounds for the area of disks as well as near optimal upper bound
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79218551dabb4350ed3d156af7ffeb69
https://doi.org/10.1112/blms/bdp044
https://doi.org/10.1112/blms/bdp044
Autor:
Christopher B. Croke
Publikováno v:
Proceedings of the American Mathematical Society. 133:3663-3668
We consider compact Riemannian manifolds ( M , ∂ M , g ) (M,\partial M,g) with boundary ∂ M \partial M and metric g g on which a finite group Γ \Gamma acts freely. We determine the extent to which certain rigidity properties of ( M , ∂ M , g )
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73e8298d7e2a7e84fb2dd5fa606c3065
https://doi.org/10.1090/s0002-9939-05-07927-x
https://doi.org/10.1090/s0002-9939-05-07927-x
Publikováno v:
Journal of Mechanical Design. 126:609-616
A fully reversed (FR) sequence of rotations is defined as a series of rotations of a free rigid body about its body-fixed axes such that the rotation about each axis is fully reversed at the end of the sequence. Due to the non-commutative property of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::10f31bb6bcbb603cbdad5f82fd95f8d0
https://doi.org/10.1115/1.1758249
https://doi.org/10.1115/1.1758249
Autor:
Christopher B. Croke
Publikováno v:
Ergodic Theory and Dynamical Systems. 24:723-733
We show that the metric of non-positively curved graph manifolds is determined by its geodesic flow. More precisely, we show that if the geodesic flows of two non-positively curved graph manifolds are C 0 conjugate, then the spaces are isometric.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::056206dec6521a7ce8a6faa9f84a5bc1
https://doi.org/10.1017/s0143385703000592
https://doi.org/10.1017/s0143385703000592
Autor:
Christopher B. Croke
Publikováno v:
Communications in Analysis and Geometry. 10:467-474
We show that the volume of any Riemannian metric on a three sphere is bounded below by the length of the shortest closed curve that links its antipodal image. In particular, the volume is bounded below by the minimum of the length of the shortest clo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::028554d1fd894dc4f42827a3de065e1e
https://doi.org/10.4310/cag.2002.v10.n3.a2
https://doi.org/10.4310/cag.2002.v10.n3.a2
Autor:
R. Andrew Hicks, Christopher B. Croke
Publikováno v:
Journal of the Optical Society of America. A, Optics, image science, and vision. 31(9)
Here we present a method for the coupled design of four freeform reflective surfaces that will control a bundle of rays. By this, we mean that given an input bundle of rays, we can construct an optical system that will map it to a given output bundle
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7684863eda3dbc40301a9961efc1c07e
https://pubmed.ncbi.nlm.nih.gov/25401451
https://pubmed.ncbi.nlm.nih.gov/25401451
Publikováno v:
Transactions of the American Mathematical Society. 352:3937-3956
This paper considers the boundary rigidity problem for a compact convex Riemannian manifold ( M , g ) (M,g) with boundary ∂ M \partial M whose curvature satisfies a general upper bound condition. This includes all nonpositively curved manifolds and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f33141e44f71b93bc6484dea5d0487a
https://doi.org/10.1090/s0002-9947-00-02532-0
https://doi.org/10.1090/s0002-9947-00-02532-0
Autor:
Christopher B. Croke, Bruce Kleiner
Publikováno v:
Topology. 39(3):549-556
We construct a pair of finite piecewise Euclidean 2-complexes with nonpositive curvature which are homeomorphic but whose universal covers have nonhomeomorphic ideal boundaries, settling a question of Gromov.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b21ab684eff88bd8994c6a49deafd1bc