scholarly journals The Continuity Method on Fano Fibrations

Author(s):  
Yashan Zhang ◽  
Zhenlei Zhang
2018 ◽  
Vol 140 (5) ◽  
pp. 1253-1276 ◽  
Author(s):  
Chen Jiang
Keyword(s):  

2012 ◽  
Vol 148 (6) ◽  
pp. 1985-2003 ◽  
Author(s):  
Chi Li

AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the moment polytope.


2016 ◽  
Vol 25 ◽  
pp. S233-S234
Author(s):  
J. Stevenson ◽  
A. Kwon ◽  
G. Scalia

1986 ◽  
Vol 32 (112) ◽  
pp. 446-454 ◽  
Author(s):  
Louis Reynaud ◽  
Michel Vallon ◽  
Anne Letreguilly

AbstractThe optimum continuation of series of mass-balance measurements and their extension to unmonitored glaciers are important problems in contemporary glaciology. For this purpose, two new practical survey methods are proposed, based on the linear-balance variations model of Lliboutry (1974). The first method is asimplified applicationof the linear model that uses only a data set limited to selected fixed-measurement sites. It was developed to obtain the mass-balance variation in cases where data are too scarce to obtain the global mass balance or to apply the Lliboutry algorithm. Thissimplified linear modelis used with the 8 years’ of surveys on glacier d’Argentière. The second method uses thecontinuity equationto derive the mass balance of a glacier sector delimited by two cross-profiles where the surface velocities, surface altitudes, and depths are known. By using thiscontinuity method, the entire mass-balance series is established for a sector of glacier de Gébroulaz (Vanoise area, France) from 1908 to 1950, as well as for two sectors of Unteraargletscher (Oberland, Switzerland) from 1924 to 1981.


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