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Closed Characteristics on Asymmetric Convex Hypersurfaces in R 2n and the Corresponding Pinching Conditions

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Abstract

In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed characteristics on convex compact hypersurfaces in R 2n pinched by not necessarily symmetric convex compact hypersurfaces.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, P. R. China

    Yu Jun Dong*

  2. Nankai Institute of Mathematics, Nankai University, Tianjin, 300071, P. R. China

    Yu Jun Dong*

  3. Nankai Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Yi Ming Long**

Authors
  1. Yu Jun Dong*
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  2. Yi Ming Long**
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Correspondence to Yu Jun Dong*.

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*Partially supported by the 973 Program of STM, Funds of EC of Jiangsu, the Natural Science Funds of Jiangsu (BK 2002023), the Post-doctorate Funds of China, and the NNSF of China (10251001)

**Partially supported by the 973 Program of STM, NNSF, MCME, RFDP, PMC Key Lab of EM of China, S. S. Chern Foundation, and Nankai University

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Dong*, Y.J., Long**, Y.M. Closed Characteristics on Asymmetric Convex Hypersurfaces in R 2n and the Corresponding Pinching Conditions. Acta Math Sinica 20, 223 (2004). https://doi.org/10.1007/s10114-004-0360-0

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  • DOI: https://doi.org/10.1007/s10114-004-0360-0

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