https://neckpinch.com/authors/charles-baker/New arXiv papers by Charles Baker, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2004.12259/arxiv:2004.12259Sun, 26 Apr 2020 00:00:00 GMTCharles Baker, Huy The Nguyen — In this paper, we prove convergence of the high codimension mean curvature flow in the sphere to either a round point or a totally geodesic sphere assuming a pinching condition between the norm squared of the second fundamental form and the norm squared of the mean curvature and the background curvature of the sphere. We show that this pinching is sharp for dimension n≥ 4 but is not sharp for dimension n=2,3. For dimension n=2 and codimension 2, we consider an alternative pinching condition which includes the normal curvature of the normal bundle. Finally, we sharpen the Chern-do Carmo-Kobayashi curvature condition for surfaces in the four sphere - this curvature condition is sharp for minimal surfaces and we conjecture it to be sharp for curvature flows in the sphere.Mean curvature flowOther curvature flowsCurvature pinchingMinimal & CMC surfaces https://neckpinch.com/papers/1605.06200/arxiv:1605.06200Fri, 20 May 2016 00:00:00 GMTCharles Baker, Huy The Nguyen — We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.Mean curvature flow