What does this research mean for the field?

The volume of any three-dimensional convex body of constant width d is bounded below by (4π/33)d³, or approximately 0.380799 d³, improving upon previous lower bounds. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Establish an improved lower bound on the volume of three-dimensional convex bodies of constant width, addressing the open 3D Blaschke–Lebesgue problem.

August 28, 2026Journal of Mathematical Analysis and ApplicationsOpen Access

An improved lower bound for the three-dimensional Blaschke–Lebesgue problem from spectral and dual perspectives

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Establish an improved lower bound on the volume of three-dimensional convex bodies of constant width, addressing the open 3D Blaschke–Lebesgue problem.
Formulated the volume minimization problem through support functions.
Derived spectral estimates using spherical harmonics and Bochner's formula.
Interpreted the lower bound within a Lagrange dual framework for concave quadratic minimization.
Established a new analytical lower bound of (4π/33)d³ ≈ 0.380799d³ for the volume of any 3D body of constant width d.
Improved Chakerian's longstanding lower bound of approximately 0.364916d³, narrowing the gap to the conjectured Meissner tetrahedra volume of ≈ 0.419860d³.

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Implication

Theoretical analysis demonstrates an improved volume lower bound for three-dimensional bodies of constant width, indicating progress toward resolving Meissner's conjecture.

Cite This Study

Akatsuki Nishioka (2026) studied this question.

synapsesocial.com/papers/6a914599d15324a1df3a8eec https://doi.org/10.1016/j.jmaa.2026.131038

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Implication

Theoretical analysis demonstrates an improved volume lower bound for three-dimensional bodies of constant width, indicating progress toward resolving Meissner's conjecture.

An improved lower bound for the three-dimensional Blaschke–Lebesgue problem from spectral and dual perspectives

Key Points

Discussion

Implication

Cite This Study

An improved lower bound for the three-dimensional Blaschke–Lebesgue problem from spectral and dual perspectives

Key Points

Discussion

Implication

Cite This Study