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math.DG2026

Monotonicity formulas for minimal submanifolds involving Möbius transformations

Doanh Pham

For a minimal submanifold of the Euclidean space, we prove monotonicity formulas for its (weighted) volume within images of concentric balls under Möbius transformations.

math.DG2026

A monotonicity formula for anisotropic minimal hypersurfaces

Doanh Pham

Under a sign assumption on the Minkowski norm, we prove a monotonicity formula for anisotropic minimal hypersurfaces in Euclidean space.

math.DG2024

A logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector

Doanh Pham

In this paper, we prove a logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector in a manifold with nonnegative sectional curvature.