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arxiv: 2206.08302 · v2 · pith:TXUXL5J6new · submitted 2022-06-16 · 🧮 math.DG

The prescribed point area estimate for minimal submanifolds in constant curvature

Keaton Naff , Jonathan J. Zhu This is my paper
classification 🧮 math.DG
keywords estimateareaminimalpointprescribedprovesubmanifoldsanalogous
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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 cases, we also prove the corresponding estimate in the sphere. Our estimates are analogous to those of Brendle and Hung in the Euclidean setting.

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    Proves monotonicity formulas for weighted volumes of minimal submanifolds under Möbius images of concentric balls.