Research

My research in pure mathematics is primarily focused on Lagrangian mean curvature flow, a phenomenon whereby Lagrangian submanifolds in Kahler-Einstein manifolds are allowed to evolve according to their mean curvature. My main contribution to the subject has been the study of Lagrangian mean curvature flow in Fano manifolds, in particular the complex projective plane CP2. Here I demonstrated that Lagrangian tori satisfying a symmetry condition exist for all time under a flow with surgery and converge to a minimal torus in infinite time. This was the first example in the literature of Lagrangian mean curvature flow with surgery and answered a Thomas-Yau type conjecture. For those wanting to read about this but not wishing to wade through 125 pages of a doctoral thesis, please see the corresponding paper on the arXiv which covers the same material in abridged format in 35 pages.

I have also worked on Lagrangian mean curvature flow with boundary with my collaborators Ben Lambert and Albert Wood. We showed the existence of a boundary condition for LMCF and studied some basic examples.

Publications:

C.G. Evans, Lagrangian mean curvature flow in the complex projective plane (2022), Doctoral thesis, University College London [Available through UCL]

C.G. Evans, B. Lambert and A. Wood, Lagrangian mean curvature flow with boundary (2019), to appear in Calc. Var. and PDE [arXiv pre-print]

C.G. Evans, J.D. Lotay and F. Schulze - Remarks on the self-shrinking Clifford torus (2018), J. Reine Angew. Math., (Crelle's journal) [arXiv pre-print]

Pre-prints:

C.G. Evans, Lagrangian mean curvature flow in the complex projective plane (2022), [arXiv pre-print]

In order to maintain some semblence of chronology, publications are dated according to when the preprint was published, not when they were published in journals.