54 citations · 203 across the 24 of their papers we have counts for
25 papers
The Strominger system in the square of a Kähler class
Tristan C. Collins, Sebastien Picard, Shing-Tung Yau
We study the Strominger system with fixed balanced class. We show that classes which are the square of a Kähler metric admit solutions to the system for vector bundles satisfying t…
Flows of -Structures associated to Calabi-Yau Manifolds
Sébastien Picard, Caleb Suan
We establish a correspondence between a parabolic complex Monge-Ampère equation and the -Laplacian flow for initial data produced from a Kähler metric on a complex - or …
Stability of the Type IIA flow and its applications in symplectic geometry
Teng Fei, Duong H. Phong, Sebastien Picard +1
In this paper the dynamical stability of the Type IIA flow with no source near its stationary points is established. These stationary points had been shown previously by the author…
Special Lagrangian cycles and Calabi-Yau transitions
Tristan C. Collins, Sergei Gukov, Sebastien Picard +1
We construct special Lagrangian 3-spheres in non-Kähler compact threefolds equipped with the Fu-Li-Yau geometry. These non-Kähler geometries emerge from topological transitions of…
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…
Anomaly Flow and T-Duality
Teng Fei, Sebastien Picard
In this paper, we study the dual Anomaly flow, which is a dual version of the Anomaly flow under T-duality. A family of monotone functionals is introduced and used to estimate the…
New curvature flows in complex geometry
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
This is a survey of some of the recent developments on the geometric and analytic aspects of the Anomaly flow. It is a flow of -forms on a -fold which was originally moti…
A flow of conformally balanced metrics with Kähler fixed points
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally…
Fu-Yau Hessian Equations
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope . Actually we obtain at the same time a solution of the open case , an improved solution of the k…
The Anomaly flow over Riemann surfaces
Teng Fei, Zhijie Huang, Sebastien Picard
We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a crite…
The Anomaly flow on unimodular Lie groups
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
The Hull-Strominger system for supersymmetric vacua of the heterotic string allows general unitary Hermitian connections with torsion and not just the Chern unitary connection. Sol…
A Construction of Infinitely Many Solutions to the Strominger System
Teng Fei, Zhijie Huang, Sebastien Picard
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely…
The Anomaly flow and the Fu-Yau equation
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter . This implies both results of Fu…
Anomaly flows
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
The Anomaly flow is a flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced conditio…
Concavity of the Lagrangian Phase Operator and Applications
Tristan C. Collins, Sebastien Picard, Xuan Wu
We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if is a compact domain in o…
The Fu-Yau equation with negative slope parameter
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system,…
Geometric flows and Strominger systems
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
A geometric flow on -forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. T…
A second order estimate for general complex Hessian equations
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
We derive a priori estimates for the -plurisubharmonic solutions of general complex Hessian equations with right-hand side depending on gradients.
On estimates for the Fu-Yau generalization of a Strominger system
Duong H. Phong, Sebastien Picard, Xiangwen Zhang
We study an equation proposed by Fu and Yau as a natural -dimensional generalization of a Strominger system that they solved in dimension . It is a complex Hessian equation w…