Analytic Continuation Of Convex Bodies And Funk's Characterization Of The Sphere

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Analytic Continuation Of Convex Bodies And Funk's Characterization Of The Sphere (Make Corrections) (1 citation)
Eric L. Grinberg, Eric Todd Quinto

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Abstract: A celebrated theorem of P. Funk [F] states that an origin-centered star body in R³ is determined by the areas of its central hyperplane cross-sections. In particular, if all these concurrent sections have the same area then the surface must be a sphere. It is natural to try to strengthen the theorem by using a smaller class of planes. It is evident that a lower-dimensional class of hyperplanes, e.g., planes passing through an axis, does not suce, but a proper open subset of planes appears... (Update)

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BibTeX entry: (Update)

E. L. Grinberg and E. T. Quinto. Analytic continuation of convex bodies and Funk's characterization of the sphere. Preprint. GEOMETRIC TOMOGRAPHY--CORRECTIONS AND UPDATE 23 http://citeseer.ist.psu.edu/408566.html More

@misc{ grinberg-analytic,
  author = "E. Grinberg and E. Quinto",
  title = "Analytic continuation of convex bodies and Funk's characterization of the
    sphere",
  note = "Preprint. GEOMETRIC TOMOGRAPHY--CORRECTIONS
    AND UPDATE 23",
  url = "citeseer.ist.psu.edu/408566.html" }

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