@article{HermannHumbert2020,
  author    = {Hermann, Andreas and Humbert, Emmanuel},
  title     = {Mass functions of a compact manifold},
  series = {Journal of geometry and physics : JGP},
  volume    = {154},
  journal   = {Journal of geometry and physics : JGP},
  publisher = {Elsevier},
  address   = {Amsterdam [u.a.]},
  issn      = {0393-0440},
  doi       = {10.1016/j.geomphys.2020.103650},
  pages     = {14},
  year      = {2020},
  abstract  = {Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M).},
  language  = {en}
}
@article{HermannHumbert2016,
  author    = {Hermann, Andreas and Humbert, Emmanuel},
  title     = {About the mass of certain second order elliptic operators},
  series = {Advances in mathematics},
  volume    = {294},
  journal   = {Advances in mathematics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0001-8708},
  doi       = {10.1016/j.aim.2016.03.008},
  pages     = {596 -- 633},
  year      = {2016},
  abstract  = {Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved.},
  language  = {en}
}