arXiv subjects

Saman Habibi Esfahani

Publications and source records attributed to Saman Habibi Esfahani.

5 recordsLinked to original sources

arXiv2026

On the Donaldson-Scaduto conjecture

Motivated by $G_2$-manifolds with coassociative fibrations in the adiabatic limit, Donaldson and Scaduto conjectured the existence of associative submanifolds homeomorphic to a three-holed $3$-sphere with three asymptotically cylindrical ends in the $G_2$-manifold $X \times \mathbb{R}^3$, or equivalently similar special Lagrangians in the Calabi-Yau 3-fold $X \times \mathbb{C}$, where $X$ is an $A_2$-type ALE hyperkähler 4-manifold. We prove this conjecture by solving a real Monge-Ampère equation with a singular right-hand side, which produces a potentially singular special Lagrangian. Then, we prove the smoothness and asymptotic properties for the special Lagrangian using inputs from geometric measure theory. The method produces many other asymptotically cylindrical $U(1)$-invariant special Lagrangians in $X\times \mathbb{C}$, where $X$ arises from the Gibbons-Hawking construction.

math.DG↗

arXiv2025

Uniqueness in the local Donaldson-Scaduto conjecture

The local Donaldson-Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi-Yau 3-fold $X \times \mathbb{R}^2$, where $X$ is an ALE hyperkähler 4-manifold of $A_2$-type. The existence of this special Lagrangian has previously been proved. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.

math.DG↗

arXiv2024

Fueter sections and $\mathbb{Z}_2$-harmonic 1-forms

Motivated by a conjecture of Donaldson and Segal on the counts of monopoles and special Lagrangians in Calabi-Yau 3-folds, we prove a compactness theorem for Fueter sections of charge 2 monopole bundles over 3-manifolds: Let $u_k$ be a sequence of Fueter sections of the charge 2 monopole bundle over a closed oriented Riemannian 3-manifold $(M,g)$, with $L^\infty$-norm diverging to infinity. Then a renormalized sequence derived from $u_k$ subsequentially converges to a non-zero $\mathbb{Z}_2$-harmonic 1-form $\mathcal{V}$ on $M$ in the $W^{1,2}$-topology.

math.DG↗

arXiv2023

Towards a monopole Fueter Floer homology I: a compactness theorem

Motivated by a conjecture of Donaldson and Segal, we take a first step towards defining a new 3-manifold Floer theory, where the complex is defined by a count of Fueter sections of a hyperkähler bundle over the 3-manifold with fibers modeled on the moduli space of centered monopoles on $\mathbb{R}^3$ with charge $k \in \mathbb{Z}_{\geq 2}$. The main difficulty in defining these counts comes from the non-compactness problems. In this writing, we prove a compactness theorem in this direction in the case of $k=2$.

math.GT↗

arXiv2022

Singular Monopoles on Closed 3-Manifolds

We prove the existence of non-trivial irreducible SU(2)-monopoles with Dirac singularities on any rational homology 3-sphere, equipped with any Riemannian metric, using a gluing construction.

math.DG↗