BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pablo Mira (Universidad Politécnica de Cartagena) DTSTART:20220111T150000Z DTEND:20220111T160000Z DTSTAMP:20260423T053134Z UID:DGSTO/24 DESCRIPTION:Title: T he Bernstein problem for Weingarten surfaces\nby Pablo Mira (Universid ad Politécnica de Cartagena) as part of Differential Geometry Seminar Tor ino\n\n\nAbstract\nA surface in Euclidean $3$-space is an elliptic Weingar ten surface if its principal curvatures are related by a smooth\, symmetri c\, elliptic equation $W(k_1\,k_2)=0$. A well known open problem\, propose d for instance by Rosenberg and Sa Earp in 1994\, is to solve the Bernstei n problem for this class of surfaces\, that is: are planes the only entire elliptic Weingarten graphs? Up to now\, it is only known that the answer is positive if the Weingarten equation is uniformly elliptic\, i.e.\, if t he derivatives of $W$ with respect to $k_1$ and $k_2$ lie between two posi tive constants (for example\, minimal or CMC surfaces are uniformly ellipt ic with this terminology). This result follows from a deep theorem by L. S imon on entire graphs with quasiconformal Gauss map. In this talk we pres ent two theorems. In the first one\, we extend the solution to the Bernste in problem in the uniformly elliptic case to multigraphs\, proving that pl anes are the only complete uniformly elliptic Weingarten surfaces whose Ga uss map image lies in an open hemisphere. In the second one\, we will solv e in the affirmative the Bernstein problem for Weingarten graphs for a lar ge class of non-uniformly elliptic Weingarten equations. This is a joint w ork with Isabel Fernández and José A. Gálvez.\n LOCATION:https://researchseminars.org/talk/DGSTO/24/ END:VEVENT END:VCALENDAR