caa a22 4500 605496234 CHVBK 20210128100535.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10231-014-0402-x doi (NATIONALLICENCE)springer-10.1007/s10231-014-0402-x Critical points and geometric properties of Green's functions on open surfaces [Elektronische Daten] [Alberto Enciso, Daniel Peralta-Salas] In this paper, we consider the Green's functions of the Laplacian on an open surface $$M$$ M . Specifically, we analyze the integral curves of the gradient of the Green's function with a fixed pole as a tool to study the connections between the Green's function and the geometry of $$M$$ M . Indeed, through the analysis of the integral curves, we find a natural decomposition of the surface as the union of a disk and a $$1$$ 1 -skeleton that encodes the topology of $$M$$ M and leads to a topological upper bound for the number of critical points of the Green's function. Connections with the conformal structure of the surface are also discussed. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Green's function nationallicence Critical points nationallicence Geometric properties nationallicence Elliptic PDE nationallicence Enciso Alberto Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049, Madrid, Spain aut Peralta-Salas Daniel Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049, Madrid, Spain aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/3(2015-06-01), 881-901 0373-3114 194:3<881 2015 194 10231 https://doi.org/10.1007/s10231-014-0402-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0402-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Enciso Alberto Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049, Madrid, Spain aut NATIONALLICENCE 700 1- Peralta-Salas Daniel Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049, Madrid, Spain aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/3(2015-06-01), 881-901 0373-3114 194:3<881 2015 194 10231