Poincaré-Hopf type theorems for vector fields and 1-forms on singular varieties
Osterix and RUNX-2 expression in odontogenic myxomas and fibromyxomas
Differential equations: a dynamical approach for the Poincaré-Hopf Theorem
| Full text | |
| Author(s): |
Galvez, Jose A.
;
Mira, Pablo
;
Tassi, Marcos P.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 61, n. 4, p. 20-pg., 2022-08-01. |
| Abstract | |
We show that any compact surface of genus zero in R-3 that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of Simon's quasiconformal Bernstein theorem. The result generalizes, among others, Hopf's theorem for constant mean curvature spheres, the classification of round spheres as the only compact elliptic Weingarten surfaces of genus zero, and the uniqueness theorem for ovaloids by Han, Nadirashvili and Yuan. The proof relies on the Bers-Nirenherg representation of solutions to linear elliptic equations with discontinuous coefficients. (AU) | |
| FAPESP's process: | 20/03431-6 - Uniqueness of immersed spheres in three-dimensional Riemannian manifolds and Enneper-type hypersurfaces |
| Grantee: | Marcos Paulo Tassi |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |