By Luca Capogna
Contemporary advancements in geometric degree thought and harmonic research have resulted in new and deep effects about the regularity of the aid of measures which behave "asymptotically" (for balls of small radius) because the Euclidean quantity. A awesome function of those effects is they really represent flatness of the help by way of the asymptotic habit of the degree. Such characterizations have ended in vital new development within the learn of harmonic degree for non-smooth domain names. This quantity offers an up to date review and an advent to the study literature during this sector. The presentation follows a sequence of 5 lectures given via Carlos Kenig on the 2000 Arkansas Spring Lecture sequence on the collage of Arkansas. the unique lectures were accelerated and up to date to mirror the speedy development during this box. A bankruptcy at the planar case has been extra to supply a old standpoint. extra heritage has been incorporated to make the fabric available to complex graduate scholars and researchers in harmonic research and geometric degree thought.
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