Author

Rui Chen

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Preprint Aug 2026

Two-point estimates for the logarithmic p-flux of the first Dirichlet p-eigenfunction

Let $u>0$ be the first Dirichlet $p$-eigenfunction on a bounded convex domain $\Omega\subset\mathbb R^N$, and set \[ X_\Omega:=|\nabla\log u|^{p-2}\nabla\log u. \] We study whether the sharp one-dimensional two-point modulus for $X_\Omega$, which for $p=2$ reduces to the logarithmic-gradient estimate of Andre...

Rui Chen · 0 citations

Preprint Sep 2026

The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds

Let $M$ be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type $(1,1)$, with constant $2$ for real-valued functions. Consequently, it is bounded on $L^p(M)$ for $1<p\leq2$, with constants depending only on $p$, which proves the Coulhon--Duong conjecture. The proof uses an obst...

Rui Chen, Ren-Jin Jiang, Bo Li et al. · 1 citation