On two recent conjectures in convex geometry

TL;DR

This paper addresses two recent conjectures in convex geometry, providing disproofs that challenge previous assumptions and advance understanding in the field.

Contribution

The paper introduces counterexamples that disprove two recent conjectures, offering new insights into convex geometric properties.

Findings

Both conjectures are false based on constructed counterexamples

The disproofs clarify limitations of current convex geometry theories

Results impact future research directions in convex geometric analysis

Abstract

Two conjectures recently proposed by one of the authors are disproved