An example on null sets of parabolic measures

Jang Mei Wu

Research output: Contribution to journalArticlepeer-review


A set E on the real line of Hausdorff dimension 1 is constructed, such that the graph of E on the boundary of any C2 domain (t > τ(x)), or on the boundary of any Lip 1/2 domain (x > χ(t)), is null with respect to the parabolic measure associated with any parabolic operator L = a(x, t)∂2/∂x2 − ∂/∂t on R2; a is Hölder continuous and 0 < Λ1 ≥ a ≥ Λ2 < ∞ for some constants Λ1 and Λ2.

Original languageEnglish (US)
Pages (from-to)949-961
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Dec 1989

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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