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Bio
I work in mathematical analysis. My research deals with complex analysis, Fourier analysis and geometric measure theory. Particularly, I am interested in the relationship between analytic notions such as analytic capacity or harmonic measure, and geometric concepts like rectifiability. In a sense, analytic capacity measures how much a set in the plane is visible or invisible for analytic functions. On the other hand, rectifiability tells you if a set is contained in a countable collection of curves with finite length. Around 2002 I proved that analytic capacity is semiadditive. This was an open problem since the early 1960s. More recently I have studied related problems in higher dimensions. In particular, in a collaboration with F. Nazarov and A. Volberg I have proved the so called David-Semmes conjecture in the codimension 1 case. This result has important applications to the study of harmonic measure, which is another of my main interests.
Research Interests
Papers共 151 篇Author StatisticsCo-AuthorSimilar Experts
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INTERNATIONAL MATHEMATICS RESEARCH NOTICESno. 8 (2024): 6579-6605
arxiv(2024)
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arXiv (Cornell University) (2023)
Archive for Rational Mechanics and Analysisno. 3 (2023)
arXiv (Cornell University) (2023)
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSISno. 3 (2023)
arXiv (Cornell University) (2023)
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSISno. 3 (2023): 1-59
Communications on Pure and Applied Mathematicsno. 2 (2023): 305-336
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Author Statistics
#Papers: 150
#Citation: 3955
H-Index: 30
G-Index: 58
Sociability: 5
Diversity: 0
Activity: 1
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