par Nguyen, Manh Tien 
Référence Transactions of the American Mathematical Society, 376, 8, page (5899-5921)
Publication Publié, 2023
Référence Transactions of the American Mathematical Society, 376, 8, page (5899-5921)
Publication Publié, 2023
Article révisé par les pairs
| Résumé : | We prove that in a Riemannian manifold M, each function whose Hessian is proportional the metric tensor yields a weighted monotonicity theorem. Such function appears in the Euclidean space, the round sphere Sn and the hyperbolic space Hn as the distance function, the Euclidean coordinates of Rn+1 and the Minkowskian coordinates of Rn,1. Then we show that weighted monotonicity theorems can be compared and that in the hyperbolic case, this comparison implies three SO(n,1)-distinct unweighted monotonicity theorems. From these, we obtain upper bounds of the Graham–Witten renormalised area of a minimal surface in term of its ideal perimeter measured under different metrics of the conformal infinity. Other applications include a vanishing result for knot invariants coming from counting minimal surfaces of Hn and a quantification of how antipodal a minimal submanifold of Sn has to be in term of its volume. |
