Mean Curvature Flow with Boundary
Mean Curvature Flow with Boundary
We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under very mild hypotheses.
43 pages
Mathematics - Differential Geometry, wedge, regularity, Global submanifolds, Flows related to mean curvature, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, integral Brakke flow with boundary, boundary, mean curvature flow, Differential Geometry (math.DG), FOS: Mathematics, Nonlinear parabolic equations, 53C44 (Primary) 49Q20 (Secondary )
Mathematics - Differential Geometry, wedge, regularity, Global submanifolds, Flows related to mean curvature, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, integral Brakke flow with boundary, boundary, mean curvature flow, Differential Geometry (math.DG), FOS: Mathematics, Nonlinear parabolic equations, 53C44 (Primary) 49Q20 (Secondary )
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