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math.AP2024
On a conjecture of a Pólya functional for triangles and rectangles
Rodrigo Bañuelos, Phanuel Mariano
We consider the functional given by the product of the first Dirichlet eigenvalue and the torsional rigidity of planar domains normalized by the area. This scale invariant function…
math.AP2018
On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds
Fabrice Baudoin, Maria Gordina, Phanuel Mariano
In this note we show how results in \cite{BaudoinBonnefont2016, BaudoinGarofalo2013, CoulhonJiangKoskelaSikora2017} yield the Cheng-Yau estimate on two classes of sub-Riemannian ma…