Sione Ma‘u

activity

20062024

most citedTransfinite diameter on complex algebraic varieties

7 citations · 11 across the 9 of their papers we have counts for

collaborators

10 papers

math.NA2024

On the approximation properties of fast Leja points

Sione Ma`u

Fast Leja points on an interval are points constructed using a discrete modification of the algorithm for constructing Leja points. Not much about fast Leja points has been proven…

math.CV2021

Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula

Sione Ma`u

We study Chebyshev constants and transfinite diameter on the graph of a polynomial mapping $f : C^{2} \to C^{2}$ . We show that two transfinite diameters of a compact…

math.CV2019★ 1 cited

Extremal functions for real convex bodies: simplices, strips, and ellipses

Sione Ma`u

We present an explicit method to compute the (Siciak-Zaharjuta) extremal function of a real convex polytope in terms of supporting simplices and strips. We use this to give a new p…

math.CV2019★ 2 cited

Transfinite diameter with generalized polynomial degree

Sione Ma`u

We prove a Chebyshev transform formula for a notion of (weighted) transfinite diameter that is defined using a generalized notion of polynomial degree. We also generalize Leja poin…

math.CV2018

Lelong classes of plurisubharmonic functions on an affine variety

Jesse hart, Sione Ma`u

We study the Lelong classes $L (V), L^{+} (V)$ of psh functions on an affine variety $V$ . We compute the Monge-Ampère mass of these functions, which we use to define…

math.CV2017

Okounkov bodies and transfinite diameter

Sione Ma`u

We present an explicit calculation of an Okounkov body associated to an algebraic variety. This is used to derive a formula for transfinite diameter on the variety. We relate this…

math.CV2015

A weighted extremal function and equilibrium measure

Len Bos, Norman Levenberg, Sione Ma`u +1

Let $K = R^{n} \subset C^{n}$ and $Q (x) := \frac{1}{2} lo g (1 + x^{2})$ where $x = (x_{1}, ..., x_{n})$ and $x^{2} = x_{1}^{2} + \dots + x_{n}^{2}$ . Utilizing extremal functions for convex bodies in ${…

math.AG2014★ 7 cited

Transfinite diameter on complex algebraic varieties

David A. Cox, Sione Ma`u

We use methods from computational algebraic geometry to study Chebyshev constants and the transfinite diameter of a pure $m$ -dimensional affine algebraic variety in $C^{n}$ …

math.AG2013★ 1 cited

Chebyshev constants, transfinite diameter, and computation on complex algebraic curves

Waisiki Baleikorocau, Sione Ma`u

Notions of directional Chebyshev constant and transfinite diameter have recently been studied on certain algebraic curves in $C^{2}$ . The theory is extended here to curves i…

math.CV2006

Complex Monge-Ampere of a Maximum

Eric Bedford, Sione Ma`u

We give a formula for the complex Monge-Ampere operator applied to the maximum of a finite number of functions.