Abstract
Our basic question is: What open, orientable surfaces of finite type occur as leaves with polynomial growth in what closed 3-manifolds? This question is motivated by other work of the authors. It is proven that every such surface so occurs for suitable C ∞ {C^\infty } foliations of suitable closed 3-manifolds and for suitable C 1 {C^1} foliations of all closed 3-manifolds. If the surface has no isolated nonplanar ends it also occurs for suitable C ∞ {C^\infty } foliations of all closed 3-manifolds. Finally, a large class of surfaces with isolated nonplanar ends occurs in suitable C ∞ {C^\infty } foliations of all closed, orientable 3-manifolds that are not rational homology spheres.
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