query: Removing Singularity of real bounded harmonic in punctured disk.
positive_passages.docid: 26353
positive_passages.text: Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
negative_passages.docid: 137045
negative_passages.text: The estimate of real and imaginary part of a holomorphic function
negative_passages.docid: 108846
negative_passages.text: Estimate of analytic function in a unit disk
negative_passages.docid: 56983
negative_passages.text: Square of a function with an essential singularity
negative_passages.docid: 64481
negative_passages.text: Characterizing all mobius transformations from unit disk to itself.
negative_passages.docid: 31736
negative_passages.text: Removable singularities and an entire function
negative_passages.docid: 51577
negative_passages.text: Non-existence of a bijective analytic function between annulus and punctured disk
negative_passages.docid: 13755
negative_passages.text: Is there a harmonic function in the whole plane that is postive everywhere?
negative_passages.docid: 123235
negative_passages.text: A smooth vector field on $S^2$ vanishing at a single point
negative_passages.docid: 102914
negative_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 41207
negative_passages.text: Conformal Map from Vertical Strip to Unit Disc
negative_passages.docid: 112517
negative_passages.text: Proving bounds of a harmonic series
negative_passages.docid: 31672
negative_passages.text: $L^p$-norm of the gradient of a harmonic function.
negative_passages.docid: 63953
negative_passages.text: Essential singularity
negative_passages.docid: 76147
negative_passages.text: Bounding holomorphic function at 0 given other bounds
negative_passages.docid: 79861
negative_passages.text: Induced metric on a null hypersurface
negative_passages.docid: 140972
negative_passages.text: Uniform convergence of harmonic functions to $0$ on compact subsets