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9781470484354 Academic Inspection Copy

On the Density Problem in the Parabolic Space

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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Andrea Merlo, Basque Foundation for Science, Bilbao, Spain. Mihalis Mourgoglou, Basque Foundation for Science, Bilbao, Spain. Carmelo Puliatti, Universidad del Pais Vasco, Leioa, Spain
Chapters; 1. Introduction; 2. Preliminaries and notation; 3. Marstrand's theorem and the structure of uniform measures; 4. Marstrand-Mattila rectifiability criterion; 5. Moments and their expansion; 6. Uniform measures of dimension $n 1$ and quadratic surfaces; 7. Structure of non-degenerated uniform measures; 8. Proof of $1$-codimensional Preiss's theorem; 9. Weak constant density implies bilateral weak geometric lemma; A. Proof of \cref{TH:FAILUREPREISS}; B. Taylor expansion of area on quadratic $t$-cones
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