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results from algebraic geometry and from the geometry of numbers. Iwaniec’s paper gives a broad picture of
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author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry
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analytic geometry. After studying the material, the reader will have a good understanding of basic geometry
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presents also various applications. The main analytic tool is the analytic localization technique in local
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One of the basic ideas in differential geometry is that the study of analytic properties of certain
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important in many applications, such as material sciences, image processing and differential geometry. The
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theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic
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differential equations, complex analysis in several complex variables, and differential geometry. While the PDE
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