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Strichartz-Tse LpL^p-Integrability on the Sierpinski Gasket

Energy measures of any two nonconstant harmonic functions on the standard Sierpinski gasket are mutually absolutely continuous. Strichartz and Tse reported numerical evidence that the Radon-Nikodym densities are LpL^p-integrable for 1<p<log⁡15/log⁡91 < p < \log 15 / \log 9. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

Result
Proved
Status
Resolved
AI contribution
AI-assisted
Method
Argument
Field
Fractal analysis
Posed by
Robert S. Strichartz, Samuel Tse
Year posed
2010
Years open
16y
Solved
2026-07-24
Model
GPT-5.6
Vendor
OpenAI
Collaborators
Konstantinos Tsougkas
Verification
Unreviewed
Publication
Preprint
Significance
10 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

The acknowledgement says the work was developed with assistance from the model, used to explore ideas and support aspects of the technical development and the writing, with all results and arguments independently verified by the author.

Verification

Single-author arXiv preprint; not yet peer-reviewed.

Sources

Changelog3 changes
  • Matarisvanset Year posed to “2010”, also Significance note, More links
  • Rasmus Lindahlchanged Name from “Strichartz-Tse L^p-Integrability on the Sierpinski Gasket” to “Strichartz-Tse $L^p$-Integrability on the Sierpinski Gasket”
  • Rasmus Lindahlchanged Name from “Strichartz-Tse $L^p$-Integrability on the Sierpinski Gasket” to “Strichartz-Tse L^p-Integrability on the Sierpinski Gasket”

Discussion