88 citations · 178 across the 20 of their papers we have counts for
22 papers
Anisotropic calibrations, Fueter maps and mirror symmetry
Kotaro Kawai, Tommaso Pacini
Let be a Riemannian manifold. Choose a pair , where is a calibration and is a calibrated distribution. Using these data, we define a 1-parameter family of fo…
Pluripotential theory and special holonomy, I: Hodge decompositions and lemmata
Tommaso Pacini, Alberto Raffero
Let be a compact torsion-free 7-manifold or Calabi-Yau 6-manifold. We prove Hodge decomposition theorems for the operators, introduced by Harvey and Lawson, which…
Pluri-potential theory, submersions and calibrations
Tommaso Pacini
We present a systematic collection of results concerning interactions between convex, subharmonic and pluri-subharmonic functions on pairs of manifolds related by a Riemannian subm…
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 data. As a special case, we obtain a second variation formula for variatio…
Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds
Tommaso Pacini
We show that, in toric Kaehler geometry, the sign of the Ricci curvature corresponds exactly to convexity properties of the volume functional. We also discuss analogous relationshi…
Pluri-subharmonic functions on complex tori, Ricci curvature and convexity
Tommaso Pacini
We show that, in toric manifolds, one can characterize the sign of the Ricci curvature in terms of the convexity of the volume functional. More generally we discuss relationships b…