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• W3111985369 abstract "Abstract An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in compact and non-compact settings, we provide new proofs which are both elementary and short. Moreover, we employ our method to obtain constant rank theorems for homogeneous and non-homogeneous curvature equations in new geometric settings. One of the essential ingredients for our method is a generalization of a differential inequality in a viscosity sense satisfied by the smallest eigenvalue of a linear map Brendle et al. (Acta Math 219:1–16, 2017) to the one for the subtrace. The viscosity approach provides a concise way to work around the well known technical hurdle that eigenvalues are only Lipschitz in general. This paves the way for a simple induction argument." @default.
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• W3111985369 date "2023-02-02" @default.
• W3111985369 modified "2023-10-14" @default.
• W3111985369 title "Constant rank theorems for curvature problems via a viscosity approach" @default.
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• W3111985369 doi "https://doi.org/10.1007/s00526-023-02442-5" @default.
• W3111985369 hasPublicationYear "2023" @default.
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