Author

Riccardo Caniato

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Preprint Sep 2026

Genus, Morse Index, and Area of Minimal Surfaces in Three-Manifolds

We prove that, in every closed Riemannian three-manifold $(M^3,\bar g)$, there exists a constant $C>0$ such that every closed smoothly embedded minimal surface $\Sigma\subset M$ satisfies $b_1(\Sigma;\mathbb{Z}_2)\le C\bigl(\operatorname{Ind}(\Sigma)+\operatorname{Area}(\Sigma)\bigr)$. The estimate holds without orient...

Riccardo Caniato · 0 citations

Preprint Sep 2026

High-Dimensional Families of Minimal Surfaces of Arbitrary Genus in Round Spheres

We prove the existence of arbitrarily high-dimensional families of minimal surfaces of any prescribed genus and conformal structure in even-dimensional round spheres. More precisely, let $n\geq2$ and let $\Sigma$ be any closed Riemann surface of genus $g$. We construct a sequence of degrees $d_\ell\to+\infty$ such that...

Riccardo Caniato · 1 citation · ⚡1