Author

M'arcio Batista

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Preprint Sep 2026

Overdetermined equations and support functions on the hyperbolic and de Sitter planes

We study overdetermined equations on the hyperbolic and de Sitter planes by means of the support-function representation of zero mean curvature surfaces in Lorentz--Minkowski three-space. On the hyperbolic plane, solutions of $\Delta u-2u=0$ give rise to branched spacelike maximal surfaces. We prove that, on a bounded...

M'arcio Batista, Iury Domingos · 0 citations

Preprint Sep 2026

Second Jacobi eigenvalues and spectral rigidity for surfaces in Berger spheres

In this paper, we establish an upper bound for the second eigenvalue of the scalar Jacobi operator of an arbitrary closed two-sided surface immersed in a contracted Berger sphere. The estimate involves the total squared mean curvature, the Euler characteristic, and an explicit nonpositive term determined by the angle b...

M'arcio Batista, Abraão Mendes · 0 citations

Preprint Jul 2026

Second Eigenvalue Estimates and Spectral Rigidity for Submanifolds of Compact Rank-One Symmetric Spaces

In this paper, we establish upper bounds for the second eigenvalue of the Schr\"odinger operator $L=\Delta+|\sigma|^2+k$ on $k$-dimensional closed submanifolds of the compact projective spaces $\mathbb F P^m$, where $\mathbb F\in\{\mathbb R,\mathbb C,\mathbb H\}$, as well as the Cayley projective plane. The estimates a...

M'arcio Batista, Abraão Mendes · 1 citation