Non-pluripolar energy and the complex Monge–Ampère operator
Non-pluripolar energy and the complex Monge–Ampère operator
Abstract Given a domain <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi mathvariant="normal">Ω</m:mi><m:mo>⊂</m:mo><m:msup><m:mi>ℂ</m:mi><m:mi>n</m:mi></m:msup></m:mrow></m:math> {\Omega\subset{\mathbb{C}}^{n}} we introduce a class of plurisubharmonic (psh) functions <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi mathvariant="script">𝒢</m:mi><m:mo></m:mo><m:mrow><m:mo stretchy="false">(</m:mo><m:mi mathvariant="normal">Ω</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:mrow></m:math> {{\mathcal{G}}(\Omega)} and Monge–Ampère operators <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>u</m:mi><m:mo>↦</m:mo><m:msup><m:mrow><m:mo stretchy="false">[</m:mo><m:mrow><m:mi>d</m:mi><m:mo></m:mo><m:msup><m:mi>d</m:mi><m:mi>c</m:mi></m:msup><m:mo></m:mo><m:mi>u</m:mi></m:mrow><m:mo stretchy="false">]</m:mo></m:mrow><m:mi>p</m:mi></m:msup></m:mrow></m:math> {u\mapsto[dd^{c}u]^{p}} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>p</m:mi><m:mo>≤</m:mo><m:mi>n</m:mi></m:mrow></m:math> {p\leq n} , on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi mathvariant="script">𝒢</m:mi><m:mo></m:mo><m:mrow><m:mo stretchy="false">(</m:mo><m:mi mathvariant="normal">Ω</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:mrow></m:math> {{\mathcal{G}}(\Omega)} that extend the Bedford–Taylor–Demailly Monge–Ampère …