A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
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math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.
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Prescribing geodesics and a variational problem for Riemannian metrics
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
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An Affine Invariant Minkowski Problem
The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.