Concavity for elliptic and parabolic equations in complex projective space

Concavity for elliptic and parabolic equations in complex projective space

We establish a concavity principle for solutions to elliptic and parabolic equations on complex projective space, generalizing the results of Langford and Scheuer. To our knowledge, this is the first example of a general concavity principle outside the constant sectional curvature regime, and in par...

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Bibliographic Details
Main Authors: Aryan, Shrey, Law, Michael B
Format: Journal Article
Language:English
Published: 25-03-2024
Subjects:
Mathematics - Analysis of PDEs
Mathematics - Differential Geometry
Online Access:Get full text
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Summary:We establish a concavity principle for solutions to elliptic and parabolic equations on complex projective space, generalizing the results of Langford and Scheuer. To our knowledge, this is the first example of a general concavity principle outside the constant sectional curvature regime, and in particular, our result partially answers a question raised by Korevaar in 1985 regarding the concavity of solutions to elliptic equations on manifolds with non-constant sectional curvature.
DOI:10.48550/arxiv.2403.16783