Convexity of the class of currents with finite relative energy
Duc-Viet Vu
TL;DR
This paper proves that the set of currents with finite relative energy is convex, using an integration by parts formula for relative non-pluripolar products, which is a significant theoretical advancement.
Contribution
It introduces a proof of convexity for currents with finite relative energy and develops an integration by parts formula for relative non-pluripolar products.
Findings
Established convexity of currents with finite relative energy
Developed an integration by parts formula for relative non-pluripolar products
Provides tools of independent interest for complex analysis
Abstract
We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering