Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope.

193 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry (2002, background): “Geometry of such amoebas and their applications have been studied in [5, 6, 7, 12, 13, 14, 17, 18].”
Amoebas, nonnegative polynomials and sums of squares supported on circuits (2014, background): “Taking into account the corresponding literature, in particular [27,37], an answer to this conjecture can be considered as the final piece missing to completely characterize amoebas supported on a circuit.”
Super currents and tropical geometry (2010, background): “2 These results should be compared with the results already obtained in [11].”
Amoebas of Algebraic Varieties and Tropical Geometry (2004, unknown): “Geometric properties of algebraic curves in (R∗)2.”
Discrete conformal maps and ideal hyperbolic polyhedra (2010, background): “In fact, A is an amoeba, the extended f is a Ronkin function, and the convexity of f that we have proved by elementary means follows also from a general theorem of Passare and Rullgård [26], which says that a Ronkin function”
Enumerative tropical algebraic geometry (2003, background): “The polynomial f∆ ′ min is well-defined up to a multiplication by a constant.”
Enumerative tropical algebraic geometry in R^2 (2003, methodology): “Another particularly interesting case is if F = C with the standard norm ||z|| = √ zz̄ (see [6],[16],[19], etc.”