# Non-Existence of Geometric Minimal Foliations in Hyperbolic Three-Manifolds

## TL;DR

This paper proves that closed hyperbolic three-manifolds cannot contain continuous families of minimal surfaces that are locally geometric, highlighting a fundamental geometric restriction in such manifolds.

## Contribution

It establishes the non-existence of locally geometric minimal foliations in all closed hyperbolic three-manifolds, a novel result in geometric topology.

## Key findings

- No locally geometric 1-parameter families of closed minimal surfaces exist in these manifolds.
- The result constrains the structure of minimal surfaces in hyperbolic 3-manifolds.
- Provides new insights into the geometric properties of hyperbolic three-manifolds.

## Abstract

In this paper we show that every three-dimensional closed hyperbolic manifold admits no locally geometric $1$-parameter family of closed minimal surfaces.