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July 5, 2026Open Access

Phase Transitions of Spectral Ratios Across Isometry Classes on Compact 3-Manifolds

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QZQ Zhao

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Overview

Demonstrates geometric phase transitions in compact 3-manifolds, suggesting new theoretical frameworks in spectral geometry.

Key Points

  • This research aims to establish a rigorous theory for spectral ratios and geometric phase transitions across distinct isometry classes on compact 3-manifolds.
  • Developed four independent core theorems addressing spectral criteria and phase boundaries.
  • Analyzed discontinuous spectral dynamics across the parameter plane of metric deformations.
  • Mapped applicability boundaries to geometric models without physical dynamical equations.
  • Established a spectral criterion for detecting geometric phase transitions with proven uniqueness and smoothness.
  • Showed first-order jump discontinuities in order parameters at phase boundaries, with definitive numerical examples.
  • Classified the full parameter plane, revealing new topological structures and confirming stability proofs.

Cite This Study

Q Zhao (2026) studied this question.

synapsesocial.com/papers/6a49f648f5d1d45b28800be3https://doi.org/10.5281/zenodo.21143769
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