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math.DG2022
Moving monotonicity formulae for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ba…
math.DG2022
The prescribed point area estimate for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain ca…
math.DG2022
Widths of balls and free boundary minimal submanifolds
Jonathan J. Zhu
We observe that the -dimensional width of an -ball in a space form is given by the area of an equatorial -ball. We also investigate related lower bounds for the area of a…