A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
Year: 2026
Type: preprint
Abstract: On asymptotically Schwarzschild smooth metric measure spaces modeled on the Euclidean half-space, we define a new mass-type invariant analogous to the ADM mass of an asymptotically flat manifold. We prove that this invariant is independent of the choice of admissible asymptotic coordinates. We further show that it fits into a very general framework for mass-type invariants and we also isolate static equations for smooth metric measure spaces under natural boundary conditions. For smooth metric measure spaces obtained through a generalized stereographic projection using the Green's function associated with the fractional Yamabe problem, we identify the mass with the constant term in the asymptotic expansion of the Green's function. This identification gives a geometric interpretation of the constant appearing in the fractional Yamabe problem and recasts its conjectured positivity as a positive-mass-type question.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Natural Science Foundation of China, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Nanjing University of Science and Technology, Nanjing University, Fundamental Research Funds for the Central Universities
OpenAlex ID: W7165691521