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math.DG2004★ 14 cited
An obstruction to the existence of constant scalar curvature Kähler metrics
J. Ross, R. P. Thomas
We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope for…
math.DG2001
Moment maps, monodromy and mirror manifolds
R. P. Thomas
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamilto…
math.DG2001
Special Lagrangians, stable bundles and mean curvature flow
R. P. Thomas, S. -T. Yau
We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the stability condition, and pr…