T. Pacini

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20242026

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math.DG2026

Anisotropic calibrations, Fueter maps and mirror symmetry

Kotaro Kawai, Tommaso Pacini

Let $(M, g)$ be a Riemannian manifold. Choose a pair $(α, H)$ , where $α$ is a calibration and $H$ is a calibrated distribution. Using these data, we define a 1-parameter family of fo…

math.DG2025

Pluripotential theory and special holonomy, I: Hodge decompositions and $\partial \partial ˉ$ lemmata

Tommaso Pacini, Alberto Raffero

Let $M$ be a compact torsion-free $G_{2}$ 7-manifold or Calabi-Yau 6-manifold. We prove Hodge decomposition theorems for the $d d^{I ¨} $ operators, introduced by Harvey and Lawson, which…

math.DG2024

Variation formulae for the volume of coassociative submanifolds

Tommaso Pacini, Alberto Raffero

We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of $G_{2}$ data. As a special case, we obtain a second variation formula for variatio…

Anisotropic calibrations, Fueter maps and mirror symmetry

Pluripotential theory and special holonomy, I: Hodge decompositions and ∂∂ˉ lemmata

Variation formulae for the volume of coassociative submanifolds

Pluripotential theory and special holonomy, I: Hodge decompositions and $\partial \partial ˉ$ lemmata