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Award ID contains: 2154219

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  1. ; ; (, Journal of the London Mathematical Society)
    Abstract We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result. 
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    Free, publicly-accessible full text available November 1, 2025
  2. ; ; (, International Mathematics Research Notices)
    Abstract Suppose that $$\Sigma ^{n}\subset \mathbb{S}^{n+1}$$ is a closed embedded minimal hypersurface. We prove that the first non-zero eigenvalue $$\lambda _{1}$$ of the induced Laplace–Beltrami operator on $$\Sigma $$ satisfies $$\lambda _{1} \geq \frac{n}{2}+ a_{n}(\Lambda ^{6} + b_{n})^{-1}$$, where $$a_{n}$$ and $$b_{n}$$ are explicit dimensional constants and $$\Lambda $$ is an upper bound for the length of the second fundamental form of $$\Sigma $$. This provides the first explicitly computable improvement on Choi and Wang’s lower bound $$\lambda _{1} \geq \frac{n}{2}$$ without any further assumptions on $$\Sigma $$. 
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  3. ; ; (, Analysis and Geometry in Metric Spaces)
    Abstract We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin’s differential forms to construct a Calderón reproducing formula on Rumin’s forms. 
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  4. ; (, The Journal of Geometric Analysis)
    Free, publicly-accessible full text available July 1, 2026
  5. ; (, Annali di Matematica Pura ed Applicata (1923 -))
    Free, publicly-accessible full text available April 1, 2026
  6. ; ; (, American J. of maths)
    Free, publicly-accessible full text available February 28, 2026
  7. ; ; (, Revista Matemática Iberoamericana)
    On a2m-dimensional closed manifold, we investigate the existence of prescribedQ-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we first carry out a blow-up analysis of a2mth-order PDE associated to the problem, and then apply a variational argument of min-max type. Form>1, this seems to be the first existence result for supercritical conic manifolds different from the sphere. 
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    Free, publicly-accessible full text available February 15, 2026
  8. ; ; ; (, Archive for Rational Mechanics and Analysis)
    Free, publicly-accessible full text available December 1, 2025
  9. ; ; (, The Journal of Geometric Analysis)
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  10. ; ; (, Journal of Functional Analysis)
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