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# Mixed volumes and mixed integrals

## Snapshots of modern mathematics from Oberwolfach

Mixed volumes and mixed integrals

In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from convex geometry become thereby accessible to analytic and probabilistic tools, and we can use these tools to make progress on very difficult open problems.

We discuss in this Snapshot such a functional ex- tension of some “volumes” which measure how “big” a set is. We recall the construction of “intrinsic vol- umes”, discuss the fundamental inequalities between them, and explain the functional extensions of these results.

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## Mathematical subjects

Analysis

Geometry and Topology

Senior Editor:

Carla Cederbaum

Junior Editor:

Sophia Jahns

## License

## DOI (Digital Object Identifier)

10.14760/SNAP-2018-014-EN

## Download PDF

## snapshots: overview

## Mathematical subjects

Algebra and Number Theory

Analysis

Didactics and Education

Discrete Mathematics and Foundations

Geometry and Topology

Numerics and Scientific Computing

Probability Theory and Statistics

## Connections to other fields

Chemistry and Earth Science

Computer Science

Engineering and Technology

Finance

Humanities and Social Sciences

Life Science

Physics

Reflections on Mathematics