Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, pp. 149-157.

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 f/z ¯=|f| α , 0<α<1, and f(0)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.

DOI: 10.1016/j.anihpc.2011.02.001
Classification: 35R45, 32F45, 32Q60, 32Q65, 35B05
Keywords: Differential inequality, Almost complex manifold
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     title = {Some nonlinear differential inequalities and an application to {H\"older} continuous almost complex structures},
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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, Volume 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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