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- W2956111052 abstract "Let $$Omega subset {mathbb {C}}^n$$ be a bounded pseudoconvex domain. We define the Diederich–Fornæss index with respect to a family of functions to be the supremum over the set of all exponents $$0<eta <1$$ such that there exists a function $$rho _eta $$ in this family that is comparable to $$-{{,mathrm{dist},}}(z,bOmega )$$ on $$Omega $$ and such that $$-(-rho _eta )^eta $$ is plurisubharmonic on $$Omega $$ . We first prove that computing the Diederich–Fornæss index with respect to the family of upper semi-continuous functions is the same as computing the Diederich–Fornæss index with respect to the family of Lipschitz functions. When the boundary of $$Omega $$ is $$C^k$$ , $$kge 2$$ , we prove that the Diederich–Fornæss index with respect to the family of $$C^k$$ functions is the same as the Diederich–Fornæss index with respect to the family of $$C^2$$ functions." @default.
- W2956111052 created "2019-07-12" @default.
- W2956111052 creator A5007287581 @default.
- W2956111052 date "2022-09-01" @default.
- W2956111052 modified "2023-09-26" @default.
- W2956111052 title "On competing definitions for the Diederich–Fornæss index" @default.
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- W2956111052 doi "https://doi.org/10.1007/s00209-022-03112-6" @default.
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