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arxiv: 2210.03263 · v1 · pith:WCYCKPANnew · submitted 2022-10-07 · 🧮 math.DG

Moving monotonicity formulae for minimal submanifolds in constant curvature

Keaton Naff , Jonathan J. Zhu This is my paper
classification 🧮 math.DG
keywords formulaeminimalmonotonicitysubmanifoldsballsgeodesicsetsarea
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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 ball. These monotonicity formulae involve an energy-like integral over sets which are, in general, not geodesic balls. In the Euclidean case, these sets reduce to the moving-centre balls introduced by the second author in [Zhu18].

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  1. Monotonicity formulas for minimal submanifolds involving M\"obius transformations

    math.DG 2025-04 unverdicted novelty 5.0

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