https://neckpinch.com/authors/graham-smith/New arXiv papers by Graham Smith, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2004.00054/arxiv:2004.00054Tue, 31 Mar 2020 00:00:00 GMTClaudia V. S. Magaño, Graham Smith — We construct eternal mean curvature flows of tori in perturbations of the standard unit sphere BbbS³. This has applications to the study of the Morse homologies of area functionals over the space of embedded tori in BbbS³.Mean curvature flow https://neckpinch.com/papers/1601.03437/arxiv:1601.03437Wed, 13 Jan 2016 00:00:00 GMTGraham Smith — We complete the theoretical framework required for the construction of a Morse homology theory for certain types of forced mean curvature flows. The main result of this paper describes the asymptotic behaviour of these flows as the forcing term tends to infinity in a certain manner. This result allows the Morse homology to be explicitely calculated, and will permit us to show in forthcoming work that, for a large family of smooth positive functions, F, defined over a (d+1)-dimensional flat torus, there exist at least 2^(d+1) distinct, locally strictly convex, Alexandrov-embedded hyperspheres of mean curvature prescribed at every point by F.Mean curvature flowVolume-preserving & constrained flows