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Researchers

Professor Benjamin Andrews

Professor of Mathematics

ANU College of Science

E: Ben.Andrews@anu.edu.au

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Areas of expertise

Operator Algebras And Functional Analysis 010108
Partial Differential Equations 010110
Topology 010112
Optimisation 010303
Algebraic And Differential Geometry 010102

Publications

Andrews, B, Holder, A, McCoy, J et al. 2017, 'Curvature contraction of convex hypersurfaces by nonsmooth speeds', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 727, no. 2014, pp. 169-190.
Andrews, B & Langford, M 2016, 'Two-sided non-collapsing curvature flows', Annali Della Scuola Normale Superiore di Pisa, vol. 15, no. Special, pp. 543-560.
Andrews, B, Huang, Z & Li, H 2015, 'Uniqueness for a Class of Embedded Weingarten Hypersurfaces in Sn+1', Advanced Lectures in Mathematics, vol. 33, pp. 103-114.
Andrews, B, Langford, M & McCoy, J 2015, 'Convexity estimates for surfaces moving by curvature functions', Journal of Differential Geometry, vol. 99, no. 1, pp. 47-75.
Andrews, B, Han, X, Li, H et al. 2015, 'Non-collapsing for hypersurface flows in the sphere and hyperbolic space', Annali Della Scuola Normale Superiore di Pisa, vol. 14, no. 1, pp. 331-338.
Andrews, B 2015, 'Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations', in Huai-Dong Cao, Richard Schoen, Shing-Tung Yau (ed.), Surveys in Differential Geometry Volume 19 (2014), International Press, Somerville, MA, U.S.A., pp. 1-47.
Andrews, B, Langford, M & McCoy, J 2015, 'Convexity estimates for surfaces moving by curvature functions', Journal of Differential Geometry, vol. 99, no. 1, pp. 47-75.
Andrews, B, Chen, X, Fang, H et al. 2015, 'Expansion of Co-compact convex spacelike hypersurfaces in minkowski space by their curvature', Indiana University Mathematics Journal, vol. 64, no. 2, pp. 635-662.
Andrews, B & Li, H 2015, 'Embedded constant mean curvature tori in the three-sphere', Journal of Differential Geometry, vol. 99, no. 2, pp. 169-189.
Andrews, B, Chen, X, Fang, H et al. 2015, 'Expansion of Co-compact convex spacelike hypersurfaces in minkowski space by their curvature', Indiana University Mathematics Journal, vol. 64, no. 2, pp. 635-662.
Andrews, B, Li, H & Wei, Y 2014, 'F-Stability for Self-Shrinking Solutions to Mean Curvature Flow', Asian Journal of Mathematics, vol. 18, no. 5, pp. 757-777.
Andrews, B & Langford, M 2014, 'Cylindrical estimates for hypersurfaces moving by convex curvature functions', Analysis and PDE, vol. 7, no. 5, pp. 1091-1107.
Andrews, B, Langford, M & McCoy, J 2014, 'Convexity estimates for hypersurfaces moving by convex curvature functions', Analysis & PDE (Analysis & partial differential equations), vol. 7, no. 2, pp. 407-433.
Andrews, B, McCoy, J & Langford, M 2013, 'Non-collapsing in fully non-linear curvature flows', Annales de l'Institut Henri Poincare, vol. 30, no. 1, pp. 23-32.
Andrews, B, McCoy, J & Yu, Z 2013, 'Contracting convex hypersurfaces by curvature', Calculus of Variations and Partial Differential Equations, vol. 47, no. 3-4, pp. 611-665.
Andrews, B & Clutterbuck, J 2013, 'Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue', Analysis and PDE, vol. 6, no. 5, pp. 1013-1024.
Andrews, B & Ni, L 2012, 'Eigenvalue Comparison on Bakry-Emery Manifolds', Communications in Partial Differential Equations, vol. 37, no. 11, pp. 2081-2092.
Andrews, B & McCoy, J 2012, 'Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature', Transactions of the American Mathematical Society, vol. 364, no. 7, pp. 3427-3447.
Andrews, B 2012, 'Noncollapsing in mean-convex mean curvature flow', Geometry and Topology, vol. 16, no. 3, pp. 1413-1418.
Andrews, B 2012, 'Gradient and oscillation estimates and their applications in geometric PDE', International Congress of Chinese Mathematicians (ICCM 2012), American Mathematical Society, United State of America, pp. 3-19.
Andrews, B & Chen, X 2012, 'Surfaces Moving by Powers of Gauss Curvature', Pure and Applied Mathematics Quarterly, vol. 8, no. 4, pp. 825-834.
Andrews, B & Bryan, P 2011, 'Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 653, no. 653, pp. 179-187.
Andrews, B & Clutterbuck, J 2011, 'Proof of the fundamental gap conjecture', Journal of the American Mathematical Society, vol. 24, no. 3, pp. 899-916.
Andrews, B & Bryan, P 2011, 'A comparison theorem for the isoperimetric profile under curve-shortening flow', Communications in Analysis and Geometry, vol. 19, no. 3, pp. 503-539.
Andrews, B and Clutterbuck, J, `Proof of the fundamental gap conjecture', 2011, Journal of the American Mathematical Society, vol. 24, pp 899-916
Andrews, B 2010, 'Moving surfaces by non-concave curvature functions', Calculus of Variations and Partial Differential Equations, vol. 39, no. 3-4, pp. 649-657.
Andrews, B & Baker, R 2010, 'Mean curvature flow of Pinched submanifolds to spheres', Journal of Differential Geometry, vol. 85, no. 3, pp. 357-395.
Andrews, B & Hopper, C 2010, The Ricci Flow in Riemannian Geometry: A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem, Springer, Heidelberg Germany.
Andrews, B 2004, 'Fully nonlinear parabolic equations in two space variables', arXiv (e-archive for Pre-prints, author submits), vol. 2004, no. 14 Feb, pp. 1-8.
Andrews, B & Bryan, P 2010, 'Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere', Calculus of Variations and Partial Differential Equations - Online, vol. 39, no. 3-4, pp. 419-428.
Andrews, B & Nguyen, H 2009, 'Four-manifolds with 1/4-pinched flag curvatures', Asian Journal of Mathematics, vol. 13, no. 2, pp. 251-270.
Andrews, B & Clutterbuck, J 2009, 'Time-interior gradient estimates for quasilinear parabolic equations', Indiana University Mathematics Journal, vol. 58, no. 1, pp. 351-380.
Andrews, B & Clutterbuck, J 2009, 'Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable', Journal of Differential Equations, vol. 246, no. 11, pp. 4268-4283.
Andrews, B 2007, 'Pinching estimates and motion of hypersurfaces by curvature functions', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 608, pp. 17-33.
Absil, P, Mahony, R & Andrews, B 2005, 'Convergence of the iterates of descent methods for analytic cost functions', SIAM Journal on Optimization, vol. 16, no. 2, pp. 531-547.
Andrews, B 2003, 'Classification of limiting shapes for isotropic curve flows', Journal of the American Mathematical Society, vol. 16, no. 2, pp. 443-459.
Andrews, B 2002, 'Notes on the isometric embedding problem and the Nash-Moser implicit function theorem', in Hassell A (ed.), Special Program on Spectral and Scattering Theory: Surveys in Analysis and Operator Theory, Australian National University, Canberra, Australia, pp. 157-208.
Andrews, B 2002, 'Non-Convergence and instability in the asymptotic behaviour of curves evolving by curvature', Communications in Analysis and Geometry, vol. 10, pp. 409-449.
Andrews, B 2002, 'Singularities in crystalline curvature flows', Asian Journal of Mathematics, vol. 6, no. 1, pp. 101-122.
Andrews, B 2002, 'Positively curved surfaces in the Three-sphere', in Tatsien, LI (ed.), Proceedings of the International Congress of Mathematicians, Higher Education Press, Beijing, China, pp. 221-230.
Andrews, B & Feldman, M 2002, 'Nonlocal geometric expansion of convex Planar Curves', Journal of Differential Equations, vol. 182, pp. 298-343.
Andrews, B 2001, 'Volume-Preserving Anisotropic Mean Curvature Flow', Indiana University Mathematics Journal, vol. 50, pp. 783-827.
Andrews, B 2000, 'Motion of hypersurfaces by Gauss curvature', Pacific Journal of Mathematics, vol. 195, pp. 1 - 34.
Andrews, B 1999, 'The affine curve-lengthening flow', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 506, pp. 43-83.
Andrews, B 1999, 'Gauss curvature flow: the fate of the rolling stones', Inventiones Mathematicae, vol. 138, no. 1, pp. 151-161.

Updated: 18 April 2024 / Responsible Officer: Director (Research Services Division) / Page Contact: Researchers