The global curvature estimate for the $$n-2$$ Hessian equation

Ren, Changyu; Wang, Zhizhang

doi:10.1007/s00526-023-02570-y

Calc. Var.

2023

DOI: 10.1007/s00526-023-02570-y

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The global curvature estimate for the $$n-2$$ Hessian equation

Changyu Ren,

Zhizhang Wang

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Cited by 8 publications

References 42 publications

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Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space

2023

Calc. Var.

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Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space

2023

Calc. Var.

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Starshaped compact hypersurfaces in warped product manifolds I: prescribed curvature equations

Wang

2024

Calc. Var.

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We derive global curvature estimates for closed, strictly star-shaped $$(n-2)$$ ( n - 2 ) -convex hypersurfaces in warped product manifolds, which satisfy the prescribed $$(n-2)$$ ( n - 2 ) -curvature equation with a general right-hand side. The proof can be readily adapted to establish curvature estimates for semi-convex solutions to the general k-curvature equation. Furthermore, it can also be used to prove the same estimates for k-convex solutions to the prescribed curvature measure type equations.

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A class of Hessian quotient equations in warped product manifolds

Sheng,

Xue

2024

Sci. China Math.

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The global curvature estimate for the $$n-2$$ Hessian equation

Cited by 8 publications

References 42 publications

Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space

Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space

Starshaped compact hypersurfaces in warped product manifolds I: prescribed curvature equations

A class of Hessian quotient equations in warped product manifolds

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