Logarithmic convexity of the eigenfunction of the Hessian operator in the ball

  • Authors

    • Yunhua Ye Jia Ying University
    2015-07-25
    https://doi.org/10.14419/ijams.v3i2.4979
  • Eigenfunction, Hessian Operator, Logarithmic Convexity, Strict Convexity.

  • This paper is concerned with the logarithmic convexity of the eigenfunction of the Hessian operator. It is proved that the logarithm of the eigenfunction of the Hessian operator is strictly convex in the ball.

  • References

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      [3] P.Liu, X.N.Ma and L.Xu, A Brunn-Minkowski inequatlity for the Hessian eigenvalue in three-dimensional convex domain, Adv.Math., No.225, (2010), pp.1616--1633.

      [4] X.J.Wang, A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J., No.43, (1994), pp.25--54.

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      [6] R. C. Reilly, On the Hessian of a function and the curvatures of its graph, Michigan Math.J., No.20,(1973), pp.373--383.

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  • How to Cite

    Ye, Y. (2015). Logarithmic convexity of the eigenfunction of the Hessian operator in the ball. International Journal of Advanced Mathematical Sciences, 3(2), 98-102. https://doi.org/10.14419/ijams.v3i2.4979