On the maximum principle for principal curvatures

Nina Ivochkina

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 115-126
  • ISSN: 0137-6934

Abstract

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The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.

How to cite

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Ivochkina, Nina. "On the maximum principle for principal curvatures." Banach Center Publications 33.1 (1996): 115-126. <http://eudml.org/doc/262840>.

@article{Ivochkina1996,
abstract = {The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.},
author = {Ivochkina, Nina},
journal = {Banach Center Publications},
keywords = {curvature equations; fully nonlinear differential equations},
language = {eng},
number = {1},
pages = {115-126},
title = {On the maximum principle for principal curvatures},
url = {http://eudml.org/doc/262840},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Ivochkina, Nina
TI - On the maximum principle for principal curvatures
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 115
EP - 126
AB - The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.
LA - eng
KW - curvature equations; fully nonlinear differential equations
UR - http://eudml.org/doc/262840
ER -

References

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  1. [1] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations III. Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985), 261-301. Zbl0654.35031
  2. [2] L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations IV. Starshaped compact Weingarten hypersurfaces, in: Current Topics in Partial Differential Equations, Y. Olya, K. Kasahara and N. Shimajura (eds.), Kinokunize Co., Tokyo, 1986, 1-26. Zbl0672.35027
  3. [3] L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order elliptic equations V. The Dirichlet problem for Weingarten hypersurfaces, Comm. Pure Appl. Math. 41 (1988), 47-70. Zbl0672.35028
  4. [4] N. M. Ivochkina, A description of the stability cones generated by differential operators of Monge-Ampère type, Mat. Sb. 122 (1983), 265-275 (in Russian); English transl. in Math. USSR-Sb. 50 (1985). 
  5. [5] N. M. Ivochkina, Solution of the Dirichlet problem for some equations of Monge-Ampère type, Mat. Sb. 128 (1985), 403-415 (in Russian); English transl. in Math. USSR-Sb. 56 (1987). 
  6. [6] N. M. Ivochkina, Solution of the Dirichlet problem for the m-th order curvature equations, Mat. Sb. 180 (1989), 867-887 (in Russian); English transl. in Math. USSR-Sb. 67 (1990). Zbl0695.35074
  7. [7] N. M. Ivochkina, The Dirichlet problem for m-th order curvature equations, Algebra i Analiz 2 (3) (1990), 192-217 (in Russian); English transl. in Leningrad Math. J. 2 (1991). Zbl0716.35027
  8. [8] P. L. Lions, Sur les équations de Monge-Ampère I, Manuscripta Math. 41 (1983), 1-43. Zbl0509.35036
  9. [9] N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rational Mech. Anal. 111 (1990), 153-179. Zbl0721.35018
  10. [10] N. S. Trudinger, Isoperimetric inequalities for quermassintegrals, preprint CMA-MR11-93. 

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