Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures

Coffman, Adam; Pan, Yifei

doi:10.1016/j.anihpc.2011.02.001

Coffman, Adam ; Pan, Yifei

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 149-157.

Résumé

We consider some second order quasilinear partial differential inequalities for real-valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex-valued functions $f (z)$ satisfying $\partial f / \partial \bar{z} = {| f |}^{α}$ , $0 < α < 1$ , and $f (0) \neq 0$ , there is also a lower bound for $\sup | f |$ on the unit disk. For each α, we construct a manifold with an α-Hölder continuous almost complex structure where the Kobayashi–Royden pseudonorm is not upper semicontinuous.

MR Zbl

DOI : 10.1016/j.anihpc.2011.02.001

Classification : 35R45, 32F45, 32Q60, 32Q65, 35B05
Mots-clés : Differential inequality, Almost complex manifold

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     author = {Coffman, Adam and Pan, Yifei},
     title = {Some nonlinear differential inequalities and an application to {H\"older} continuous almost complex structures},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {149--157},
     publisher = {Elsevier},
     volume = {28},
     number = {2},
     year = {2011},
     doi = {10.1016/j.anihpc.2011.02.001},
     mrnumber = {2784067},
     zbl = {1213.35409},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/}
}

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Coffman, Adam; Pan, Yifei. Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 149-157. doi : 10.1016/j.anihpc.2011.02.001. http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/

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