What question did this study set out to answer?

The aim is to estimate the Hausdorff dimension of a specific set on the boundary of the unit ball where superharmonic functions behave under a nonlinear inequality.

March 3, 2026Open Access

Boundary Growth Rates of Superharmonic Functions Satisfying a Nonlinear Inequality in the Unit Ball of ℂN

Key Points

The aim is to estimate the Hausdorff dimension of a specific set on the boundary of the unit ball where superharmonic functions behave under a nonlinear inequality.
Assessment of growth rates of Δ𝔹-superharmonic functions
Use of the Laplace–Beltrami operator associated with Bergman metrics
Analysis of conditions on parameters c, τ, and p
Determined the nonisotropic Hausdorff dimension for the specified set
Established relationships between parameters influencing growth rates
Showed that certain superharmonic functions grow faster than a prescribed order

Abstract

Let Δ𝔹 be the Laplace–Beltrami operator associated with Bergman metric on the unit ball 𝔹 of ℂN. We estimate the nonisotropic Hausdorff dimension of a set in ∂𝔹 where a positive Δ𝔹-superharmonic function u satisfying -Δ𝔹u (z) ≤c (1-|z|) τu (z) p in 𝔹 for some p∈ (0, N/ (N-1) ), τ>maxα (p−1), N (p−1) and c>0 grows faster than a prescribed order α.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Authors

Kentaro Hirata

Journals

Interdisciplinary Information Sciences

Actions

Institutions

Hiroshima University

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Boundary Growth Rates of Superharmonic Functions Satisfying a Nonlinear Inequality in the Unit Ball of ℂN

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study