In this thesis we study the deformations of special Lagrangian submanifolds X⊆ M sitting
inside a Calabi-Yau manifold (M, g, J, Ω). Let N be the normal bundle of X, and identify N∼ …

In this paper, we prove uniform curvature estimates for immersed stable free boundary
minimal hypersurfaces satisfying a uniform area bound, which generalize the celebrated …

In this paper, we study holomorphic discs in K3 surfaces and defined the open Gromov–
Witten invariants. Using this new invariant, we can establish a version of correspondence …

Suppose $ M_ {1} $ and $ M_ {2} $ are two special Lagrangian submanifolds of $\Rtn $ with
boundary that intersect transversally at one point $ p $. The set $ M_ {1}\cup M_ {2} $ is a …

Let M 7 be a smooth manifold equipped with a G 2-structure ϕ, and Y 3 be a closed compact
ϕ-associative submanifold. McLean [Deformations of calibrated submanifolds, Comm. Anal …

We provide an introduction to the theory of calibrated submanifolds through the key
examples related with special holonomy. We focus on calibrated geometry in Calabi–Yau …

In this thesis we study the geometry of manifolds with vector cross product and its
complexification. First we develop the theory of instantons and branes. For example they are …

Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special
Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in G_2 …

Let M be a topological G2-manifold. We prove that the space of infinitesimal associative
deformations of a compact associative submanifold Y with boundary in a coassociative …

Let M be a 7-manifold with a G2-structure induced by a closed 'positive'differential 3-form.
We study deformations of a compact coassociative 4-submanifold N⊂ M with non-empty …