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papers

Publications (27)

math.DG2018

Fu-Yau Hessian Equations

Duong H. Phong, Sebastien Picard, Xiangwen Zhang

We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $I^\pm^{'}$ . Actually we obtain at the same time a solution of the open case $I^\pm^{'} > 0$ , an improved solution of the…

hep-th2024

A Heterotic Hermitian--Yang--Mills Equivalence

Jock McOrist, Sebastien Picard, Eirik Eik Svanes

We consider N=1, d=4 vacua of heterotic theories in the large radius limit in which alpha' << 1. We construct a real differential operator $D = D + D ˉ$ on an extension…

math.DG2021

Stability of the tangent bundle through conifold transitions

Tristan C. Collins, Sebastien Picard, Shing-Tung Yau

Let $X$ be a compact, KÃ¤hler, Calabi-Yau threefold and suppose $X \mapsto X ⇝ X_{t}$ , for $t \in I^$ , is a conifold transition obtained by contracting finitely many…

math.DG2019

The Dirichlet Problem for the $k$ -Hessian Equation on a complex manifold

Tristan C. Collins, Sebastien Picard

We solve the Dirichlet problem for $k$ -Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a p…

math.DG2020

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-KÃ¤hler geometry which can be interpre…