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The central aim is to extend understanding of the Nirenberg problem by analyzing non-degenerate blow-up solutions with non-zero weak limits.

January 18, 2026Open Access

Nirenberg problem on high dimensional spheres : blow up with residual mass phenomenon

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The central aim is to extend understanding of the Nirenberg problem by analyzing non-degenerate blow-up solutions with non-zero weak limits.
Analyzed the subcritical approximation of the Nirenberg problem on spheres.
Described blow-up solutions including blow-up points and rates.
Computed topological contributions related to the Euler-Lagrange functional.
Identified solutions with non-zero weak limits that satisfy the Nirenberg problem.
Characterized blow-up points and their influence on topology.
Provided a partial converse by constructing non-degenerate blow-up solutions.

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This analysis explores blow-up solutions and their topology in high dimensional spheres, indicating important mathematical insights.

Ahmedou et al. (2025) studied this question.

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