Author

Tian Lan

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Preprint Sep 2026

Regularity of critical immersions for scale-invariant curvature energies in even dimensions

For immersions of a closed $2h$-dimensional manifold $\Sigma$ into $\mathbb R^m$, we consider curvature energies that are invariant under ambient isometries and dilations, with the principal term $\int_{\Sigma} \big|\nabla^{(h-1)} \vec{\mathrm{I\!I}}\big|_g^2\,d\text{vol}_g$ and lower-order submanifold invariants. Foll...

Tian Lan · 0 citations

Preprint Sep 2026

Regularity of Critical Points of Scale-Invariant Geometric Energies for Even-Dimensional Submanifolds of $\mathbb R^m$

We consider scale-invariant curvature energies for immersions of closed manifolds of even dimension $n=2h$ into $\mathbb R^m$, with principal term $\int_{\Sigma} \big|\nabla^{(h-1)} \vec{\mathrm{I\!I}}\big|_g^2\,d\text{vol}_g$ and arbitrary lower-order polynomial extrinsic invariants of the same scaling. Following the...

Tian Lan · 0 citations