# Extremal rank-one convex integrands and a conjecture of \v{S}ver\'ak

## TL;DR

This paper proves that verifying Jensen's inequality with extremal non-negative rank-one convex integrands suffices to determine if a probability measure is laminate, confirming a conjecture by vere1k.

## Contribution

It identifies a subclass of extremal integrands, truncated minors, and confirms e1ve1k's conjecture from 1992.

## Key findings

- Verification of Jensen's inequality with extremal integrands characterizes laminates.
- Identification of truncated minors as a key subclass of extremal integrands.
- Confirmation of e1ve1k's 1992 conjecture.

## Abstract

We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex integrands. We also identify a subclass of these extremal integrands, consisting of truncated minors, thus proving a conjecture made by \v{S}ver\'ak in (Arch. Ration. Mech. Anal. 119 293-300, 1992).