Superforms, supercurrents and convex geometry
Bo Berndtsson
TL;DR
This paper introduces a calculus of superforms to advance convex geometry, applying it to valuations, inequalities, and Monge-Ampère equations on convex bodies' boundaries.
Contribution
It develops a novel calculus of superforms and applies it to key problems in convex geometry, including valuations and Monge-Ampère equations.
Findings
Established a calculus of superforms for convex geometry
Applied to valuations and Alexandrov-Fenchel inequalities
Connected to Monge-Ampère equations on convex boundaries
Abstract
We develop the calculus of superforms as a tool for convex geometry. The formalism is applied to valuations on convex bodies, the Alexandrov-Fenchel inequalities and Monge- Amp\`ere equations on the boundary of convex bodies.
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Taxonomy
TopicsMathematics and Applications · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology