3 papers
math.DG2026
On the modified -equation
Ryosuke Takahashi
In this paper, we study the modified -equation introduced by Li-Shi. We first show that, on compact Kähler manifolds, the solvability of the modified -equation is equivalent…
math.DG2025
Collapsing of -Gravitational Instantons
Yu-Shen Lin, Ryosuke Takahashi
We showed that a sequence of ALH*-gravitational instantons from pairs consisting of a weak del Pezzo surface and a smooth anti-canonical divisor towards a large complex structure l…
math.DG2025
New examples of Z/2 harmonic 1-forms and their deformations
Andriy Haydys, Rafe Mazzeo, Ryosuke Takahashi
We collect a number of elementary constructions of harmonic -forms, and of families of these objects. These examples show that the branching set of a harmonic…