scholarly journals On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold

2012 ◽  
Vol 148 (6) ◽  
pp. 1985-2003 ◽  
Author(s):  
Chi Li
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Limit Behavior ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Continuity Method ◽  
Type Singularity ◽  
Moment Polytope ◽  
The Moment ◽  
Monge Ampere

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.

How Good is Stroke Volume Calculation by the Doppler Continuity Method?

2016 ◽  
Vol 25 ◽  
pp. S233-S234
Author(s):  
J. Stevenson ◽  
A. Kwon ◽  
G. Scalia
Keyword(s):  
Stroke Volume ◽  
Continuity Method ◽  
Volume Calculation

scholarly journals Mass-Balance Measurements: Problems and two New Methods of Determining Variations

1986 ◽  
Vol 32 (112) ◽  
pp. 446-454 ◽  
Author(s):  
Louis Reynaud ◽  
Michel Vallon ◽  
Anne Letreguilly
Keyword(s):  
Mass Balance ◽  
Linear Model ◽  
Continuity Equation ◽  
Survey Methods ◽  
Data Set ◽  
Continuity Method ◽  
New Methods ◽  
Two Sectors

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.

scholarly journals The Continuity Method on Minimal Elliptic Kähler Surfaces

2017 ◽  
Vol 2019 (10) ◽  
pp. 3186-3213 ◽  
Author(s):  
Yashan Zhang ◽  
Zhenlei Zhang
Keyword(s):  
Continuity Method ◽  
Kähler Surfaces

scholarly journals Smooth families of fibrations and analytic selections of polynomial hulls

1995 ◽  
Vol 52 (1) ◽  
pp. 97-105 ◽  
Author(s):  
Miran Černe
Keyword(s):  
Unit Circle ◽  
Complex Geometry ◽  
Continuity Method ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
Selection Of

Constructed are strictly increasing smooth families Σt ⊆ ∂D × C2, t ∈ [0, 1], of fibrations over the unit circle with strongly pseudoconvex fibers all diffeomorphic to the ball such that there is no analytic selection of the polynomial hull of Σ0 and which end at the product fibration . In particular these examples show that the continuity method for describing the polynomial hull of a fibration over ∂D fails even if the complex geometry of the fibers is relatively simple.

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