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Blowing-up solutions concentrated along minimal submanifolds for some supercritical Hamiltonian systems on Riemannian manifolds

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This analysis reveals blowing-up solutions in elliptic systems on Riemannian manifolds, suggesting insights into product manifold behavior.

Blowing-up solutions occur along minimal submanifolds of the product manifold, allowing for new understandings in geometry.
For any integer k ≥ 2, k-peak solutions concentrated along m-dimensional minimal submanifolds were identified.
The analysis involved an elliptic system that included Laplace-Beltrami operators on Riemannian manifolds and potential functions.
The results could enhance knowledge on supercritical systems and variations of Hamiltonian frameworks, inviting further exploration.

Chen et al. (2025) studied this question.

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View Full Paper

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Authors

This analysis reveals blowing-up solutions in elliptic systems on Riemannian manifolds, suggesting insights into product manifold behavior.

Blowing-up solutions occur along minimal submanifolds of the product manifold, allowing for new understandings in geometry.
For any integer k ≥ 2, k-peak solutions concentrated along m-dimensional minimal submanifolds were identified.
The analysis involved an elliptic system that included Laplace-Beltrami operators on Riemannian manifolds and potential functions.
The results could enhance knowledge on supercritical systems and variations of Hamiltonian frameworks, inviting further exploration.

Chen et al. (2025) studied this question.

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