Correlations between intrinsic dimension of high-dimensional spacetime and the kakeya conjecture
HU Dezhi
Abstract：This paper systematically investigates the profound connections between intrinsic dimension theory in high-dimensional spacetime and the Kakeya conjecture.By comparative analysis of their dimensional defi-nitions,mathematical frameworks,and physical implications,we reveal the inherent consistency between fractal geometric structures and high-dimensional physical models in preserving information integrity.The resolution of the three-dimensional Kakeya conjecture by Wang Hong's team not only addresses a century-old mathemat-ical challenge but also provides novel mathematical tools for string theory compactification schemes,demonstra-ting the coexistence of dimensional reduction and directional information preservation.Our findings indicate that the intrinsic dimension of high-dimensional spacetime can be unified through dynamic equilibrium of Kak-eya-type structures,achieving local expression of physical laws while maintaining global consistency.This work opens new avenues for quantum gravity theory research.
Keywords：high-dimensional spacetimeintrinsic dimensionKakeya conjectureholographic principlefractal geometryquantum gravityAdS/CFT dualitydimensional reduction
Publication Date：2025-12-30
Online Publishing Date：2025-12-19(First online date of this platform, not the publication date of the document)
Pages：6( 112-117 )