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math.AP2025
The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces
Juan Carlos Fernández, Alberto Saldaña
We study the conformal logarithmic Laplacian on the sphere, an explicit singular integral operator that arises as the derivative (with respect to the order parameter) of the confor…
math.AP2025
Fractional -curvature on the sphere and optimal partitions
Héctor A. Chang-Lara, Juan Carlos Fernández, Alberto Saldaña
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional -curvature in terms of the conformal fractional Laplacian on the…