Quantitative Stability for Yamabe minimizers on manifolds with boundary

Benjam\'in Borquez; Hanne Van Den Bosch; Rayssa Caju

Quantitative Stability for Yamabe minimizers on manifolds with boundary

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arxiv 2503.09801 v1 pith:HECDYHGS submitted 2025-03-12 math.DG

Benjamín Borquez , Rayssa Caju , Hanne Van Den Bosch This is my paper

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keywords boundaryfunctionalmanifoldsminimizersquantitativestabilityaddressesanalogous

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This paper addresses the quantitative stability for a Yamabe-type functional on compact manifolds with boundary introduced by Escobar. Minimizers of the functional correspond to scalar-flat metrics with constant mean curvature on the boundary. We prove that the deficit controls the distance to the minimizing set to a suitable power by reducing the problem to the analogous question for an effective functional on the boundary.

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Sharp quantitative stability estimates for the Brezis-Nirenberg problem
math.AP 2025-06 conditional novelty 7.0 of 10

Nearly stationary functions for the Brezis-Nirenberg problem on bounded domains lie within a sharp, dimension-dependent distance of a solution plus bubbles, and the optimal exponents are identified.

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