A multi-dimensional resolution of singularities with applications to analysis

By Tristan C. Collins, Allan Greenleaf, M. Pramanik. 2010

52 citations recorded by the source corpus.

We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions $\geq 3$. Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and elementary approach used in the contemporary algebraic geometry literature. As an application, we define a new notion of the height of real-analytic functions, compute the critical integrability index, and obtain sharp growth rate of sublevel sets. This also leads to a characterization of the oscillation index of scalar oscillatory integrals with real-analytic phases in all dimensions.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/142832337b0d6cbef4667d8465875d8d2c9625d2

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In Applied Mathematics

  1. Valentino Tosatti
  2. Tristan C. Collins
  3. B. Weinkove
  4. Xiaokui Yang
  5. Yuguang Zhang
  6. G'abor Sz'ekelyhidi
  7. Chi Li
  8. Fang Zheng

In Geometry and Topology

  1. Valentino Tosatti
  2. Tristan C. Collins
  3. B. Weinkove
  4. Xiaokui Yang
  5. Yuguang Zhang
  6. G'abor Sz'ekelyhidi
  7. Chi Li
  8. Duong H. Phong

In Mathematical Physics

  1. Valentino Tosatti
  2. Tristan C. Collins

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