# P11096: Zariski-Dense Monodromy of Singular Hyperbolic Metrics on Non-Hyperbolic Riemann Surfaces

- ID: `P11096`
- Reference: `zariski-dense-monodromy-of-singular-hyperbolic-metrics-on-non-hyperbolic-riemann-surfaces`
- Page: https://theoremdb.org/statements/P11096
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/zariski-dense-monodromy-of-singular-hyperbolic-metrics-on-non-hyperbolic-riemann-surfaces?representation=markdown
- Record maturity: Reviewed problem

## The problem

The monodromy group of every singular hyperbolic metric on a non-hyperbolic Riemann surface, in the sense of potential theory, is Zariski dense in ${\rm PSL}(2,\mathbb{R})$, confirming a conjecture of the authors.

## Status

**Resolution status:** Open.

No proof or formalization has been recorded.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `zariski-dense-monodromy-of-singular-hyperbolic-metrics-on-non-hyperbolic-riemann-surfaces`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.