query: Does there exist an area-preserving map from the hyperbolic plane to the Euclidean plane?
positive_passages.docid: 143269
positive_passages.text: Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$
negative_passages.docid: 52316
negative_passages.text: Geodesics and Curves on a Plane
negative_passages.docid: 151285
negative_passages.text: Existence of a local geodesic frame
negative_passages.docid: 77323
negative_passages.text: Existence of continuous angle function $\theta:S^1\to\mathbb{R}$
negative_passages.docid: 131589
negative_passages.text: Projections appropriate for global analysis that preserve area and that preserve distance (but not necessarily in the same projection)
negative_passages.docid: 27265
negative_passages.text: Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
negative_passages.docid: 152927
negative_passages.text: seemingly nontrivial question about covering maps and evenly covered open sets
negative_passages.docid: 50278
negative_passages.text: Explicit formula for conformal map from ellipse to unit disc (interior to interior)
negative_passages.docid: 102729
negative_passages.text: Is there an equidissection of a unit square involving irrational coordinates?
negative_passages.docid: 29014
negative_passages.text: Book recommendation on plane Euclidean geometry
negative_passages.docid: 107148
negative_passages.text: Does there always exist a continuous/smooth map from $\mathbb{R}^n$ onto a manifold $M^n$?
negative_passages.docid: 22138
negative_passages.text: Does anyone remember this article about the Euclidean Algorithm?
negative_passages.docid: 126192
negative_passages.text: Connected, locally connected, path-connected but not locally path-connected subspace of the plane
negative_passages.docid: 64481
negative_passages.text: Characterizing all mobius transformations from unit disk to itself.
negative_passages.docid: 122415
negative_passages.text: How to show every field is a Euclidean Domain.
negative_passages.docid: 118622
negative_passages.text: Local diffeomorphism from $\mathbb R^2$ onto $S^2$
negative_passages.docid: 113799
negative_passages.text: Is there an injective $C^1$ curve dense in the plane?