22 citations · 40 across the 8 of their papers we have counts for
10 papers
Stability of the tangent bundle through conifold transitions
Tristan C. Collins, Sebastien Picard, Shing-Tung Yau
Let be a compact, Kähler, Calabi-Yau threefold and suppose , for , is a conifold transition obtained by contracting finitely many d…
Bochner-Kodaira Formulas and the Type IIA Flow
Teng Fei, Duong H. Phong, Sebastien Picard +1
A new derivation of the flow of metrics in the Type IIA flow is given. It is adapted to the formulation of the flow as a variant of a Laplacian flow, and it uses the projected Levi…
Geometric Flows for the Type IIA String
Teng Fei, Duong H. Phong, Sebastien Picard +1
A geometric flow on -dimensional symplectic manifolds is introduced which is motivated by supersymmetric compactifications of the Type IIA string. The underlying structure turns…
Estimates for a geometric flow for the Type IIB string
Teng Fei, Duong H. Phong, Sebastien Picard +1
It is shown that bounds of all orders of derivative would follow from uniform bounds for the metric and the torsion 1-form, for a flow in non-Kähler geometry which can be interpret…
The Dirichlet Problem for the -Hessian Equation on a complex manifold
Tristan C. Collins, Sebastien Picard
We solve the Dirichlet problem for -Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a p…
Parabolic complex Monge-Ampere equations on compact Kahler manifolds
Sebastien Picard, Xiangwen Zhang
We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the He…