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Related Experiment Video

Updated: Jul 4, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

The Complex Plank Problem, Revisited.

Oscar Ortega-Moreno¹

¹Vienna University of Technology, Vienna, Austria.

Discrete & Computational Geometry

|February 6, 2024

Summary

This summary is machine-generated.

This study simplifies the proof for Ball's complex plank theorem, which concerns unit vectors and non-negative numbers in Euclidean spaces. The streamlined proof ensures the theorem

Keywords:

Complex geometry Covering problems Discrete geometry Functional analysis Plank problems

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Area of Science:

Linear Algebra
Functional Analysis
Geometric Analysis

Background:

Ball's complex plank theorem is a significant result in geometric analysis.
The theorem establishes the existence of a specific unit vector under certain conditions involving other unit vectors and non-negative scalars.
Original proofs can be complex, motivating the need for streamlined approaches.

Purpose of the Study:

To present a simplified and more accessible proof of Ball's complex plank theorem.
To enhance the understanding and application of this theorem in mathematical research.

Main Methods:

A streamlined approach to Ball's original proof methodology.
Focus on clarity and conciseness in mathematical exposition.
Leveraging fundamental concepts of vector spaces and scalar properties.

Main Results:

A simplified proof for Ball's complex plank theorem is successfully presented.
The streamlined proof maintains the rigor of the original theorem.
The existence of a unit vector satisfying the theorem's conditions is demonstrated through the simplified proof.

Conclusions:

The simplified proof makes Ball's complex plank theorem more approachable for researchers.
This work contributes to the pedagogical and practical understanding of the theorem.
The streamlined proof is expected to facilitate further research and applications in related mathematical fields.