Year: 2026
Type: preprint
Abstract: We prove sharp amplitude and gradient comparisons for positive solutions of a class of semilinear elliptic equations on complete manifolds under a Ricci lower bound. Equality at one point characterizes hyperbolic space and the corresponding radial solution. The local estimates are uniform in the mixing coefficients and number of terms for positive mixtures of subcritical powers. For a class of conformal compactifications defined by a source equation, we obtain sharp boundary scalar-curvature bounds and hyperbolic rigidity. We also construct non-Einstein examples whose normalization persists under small compactly supported metric perturbations.
Source: arXiv (Cornell University)
Author: Sun, Linlin
Institution: Xiangtan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G8081541980, G8418242333
OpenAlex ID: W7223844363