ORCID Profile
0000-0001-6053-5144
Current Organisation
University of Newcastle Australia
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Pure Mathematics | Partial Differential Equations | Algebraic and Differential Geometry | Topology And Manifolds | Geometry | Differential, Difference And Integral Equations |
Expanding Knowledge in the Mathematical Sciences | Mathematical sciences
Publisher: Springer Science and Business Media LLC
Date: 05-06-2013
Publisher: Elsevier BV
Date: 2023
Publisher: American Mathematical Society (AMS)
Date: 30-10-2018
DOI: 10.1090/PROC/13831
Abstract: We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of S n + 1 \\mathbb {S}^{n+1} . Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.
Publisher: Springer Science and Business Media LLC
Date: 2004
Publisher: Spandidos Publications
Date: 05-07-2016
Publisher: Walter de Gruyter GmbH
Date: 26-09-2014
Abstract: We consider contraction of convex hypersurfaces by convex speeds, homogeneous of degree one in the principal curvatures, that are not necessarily smooth. We show how to approximate such a speed by a sequence of smooth speeds for which behaviour is well known. By obtaining speed and curvature pinching estimates for the flows by the approximating speeds, independent of the smoothing parameter, we may pass to the limit to deduce that the flow by the nonsmooth speed converges to a point in finite time that, under a suitable rescaling, is round in the C 2 {C^{2}} sense, with the convergence being exponential.
Publisher: Springer Science and Business Media LLC
Date: 03-03-2017
Publisher: Springer Science and Business Media LLC
Date: 04-10-2015
Publisher: Springer Science and Business Media LLC
Date: 09-10-2015
Publisher: International Press of Boston
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 21-05-2011
Publisher: Springer Netherlands
Date: 2016
Publisher: CSIRO Publishing
Date: 1995
DOI: 10.1071/RD9950415
Abstract: This review concentrated mainly on studies of intrauterine renal function carried out in chronically-catheterized fetal sheep. In sheep, as in primates, nephrogenesis is complete before birth. Studies in the rat and neonatal puppy provide insight into the functional development of the kidney, because these species are immature at birth and there is considerable postnatal renal development. Studies of the ovine fetus provide insight into the physiological role(s) of the kidneys during intrauterine life, albeit modified by changes related to maturation.
Publisher: Indiana University Mathematics Journal
Date: 2015
Publisher: Elsevier BV
Date: 11-2008
Publisher: Elsevier BV
Date: 09-2017
Publisher: Springer Science and Business Media LLC
Date: 10-2005
Publisher: Walter de Gruyter GmbH
Date: 05-02-2021
Abstract: We consider the parabolic polyharmonic diffusion and the L 2 {L^{2}} -gradient flow for the square integral of the m -th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove that if the curvature of the initial curve is small in L 2 {L^{2}} , then the evolving curve converges exponentially in the C ∞ {C^{\\infty}} topology to a straight horizontal line segment. The same behaviour is shown for the L 2 {L^{2}} -gradient flow provided the energy of the initial curve is sufficiently small. In each case the smallness conditions depend only on m .
Publisher: Mathematical Sciences Publishers
Date: 30-05-2014
Publisher: American Mathematical Society (AMS)
Date: 07-2012
Publisher: Informa UK Limited
Date: 04-03-2018
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 02-2013
Publisher: Oxford University Press (OUP)
Date: 27-03-2008
DOI: 10.1093/QJMAM/HBN012
Publisher: International Press of Boston
Date: 2015
Publisher: Springer Science and Business Media LLC
Date: 31-05-2013
Publisher: Informa UK Limited
Date: 17-06-2016
Publisher: Springer Science and Business Media LLC
Date: 31-08-2019
Publisher: Springer Science and Business Media LLC
Date: 12-2007
Publisher: Springer Science and Business Media LLC
Date: 27-03-2014
Start Date: 01-2005
End Date: 09-2009
Amount: $353,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2012
End Date: 12-2014
Amount: $320,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2015
End Date: 12-2018
Amount: $450,800.00
Funder: Australian Research Council
View Funded ActivityStart Date: 08-2018
End Date: 05-2024
Amount: $297,478.00
Funder: Australian Research Council
View Funded Activity