3 papers
math.OA2026
Nonclassical Weyl laws and Connes' Integration for weak Lorentz ideals, II
Raphael Ponge, Yongqiang Tian
This is the second in a series of papers on Connes' integration in weak Lorentz ideals. Building on the Dixmier trace theory, Birman--Solomyak perturbation theory, and strong measu…
math.OA2026
Nonclassical Weyl laws and Connes' Integration for weak Lorentz ideals, I
Raphael Ponge, Yongqiang Tian
Motivated by nonclassical Weyl laws arising in various contexts (including Connes' approach to the Riemann Hypothesis), we develop a systematic theory of Dixmier traces and Connes'…
math.DG2013
The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian
Raphael Ponge
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the confor…