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Creators/Authors contains: "Phong, Duong"

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  1. ; ; ; (, Mathematische Zeitschrift)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; ; (, Mathematische Zeitschrift)
    Full Text Available 
  3. ; ; ; (, Communications on pure and applied mathematics)
    Diameter estimates for K\"ahler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $$L^\infty$$ estimates for the Monge-Amp\`ere equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time existence of the K\"ahler-Ricci flow and finite-time solutions when the K\"ahler class is big, as well as for special vibrations of Calabi-Yau manifolds. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Mathematische Annalen)
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  5. ; ; ; (, Analysis & PDE)
    Accepted Manuscript Full Text Available
  6. ; ; (, Annals of Mathematics)
    Accepted Manuscript Full Text Available
  7. ; ; (, Annals of Mathematics)
    Full Text Available 
  8. ; ; ; ; ; ; ; ; ; ; et al (, Notices of the American Mathematical Society)
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  9. ; ; (, Communications in Mathematical Physics)
    Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many non-compact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as non-supersymmetric deformations of the Duff–Stelle solution. 
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    Accepted Manuscript Full Text Available
  10. ; ; (, Mathematische Zeitschrift)
    A one-parameter family of coupled flows depending on a parameter $$\kappa>0$$ is introduced which reduces when $$\kappa=1$$ to the coupled flow of a metric $$\omega$$ with a $(1,1)$-form $$\alpha$$ due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for $$\kappa\not=1$$, estimates for derivatives of all orders would follow from $C^0$ estimates for $$\omega$$ and $$\alpha$$. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow in some situations, including on Riemann surfaces. Very little is known as yet about the monotonicity and convergence of flows in presence of couplings, and conditions such as $$\kappa\not=1$$ seem new and may be useful in the future. 
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    Accepted Manuscript Full Text Available