Research

Research interests

A classical question in the geometric analysis is which are the "best" metrics for a given Riemannian manifold. This subject is a significant field of research and is also at the crossroads of geometry, analysis and mathematical physics. My research interests turn around this question.

One of the most famous problems in this direction is known as the Yamabe problem. This is a classical problem in differential geometry formulated as the question of finding a non-trivial solution to a particular critical equation with the Laplace-Beltrami operator.

Inspired by that problem, I have centred my research on equations on Riemannian manifolds involving a non-linearity whose growth is critical from the point of view of the Sobolev embeddings.

Science is like magic, but real.

Publications

Alarcón, Salomón; Faya, Jorge, and Rey, Carolina. "Concentration on the Boundary and Sign-Changing Solutions for a Slightly Subcritical Biharmonic Problem". https://arxiv.org/abs/2402.14675 (2025).

Dobarro, Fernando, and Rey, Carolina A. "Einstein multiply warped products and generalized Kasner manifolds with multidimensional base." arXiv preprint arXiv:2501.02078 (2025).

Alarcón, Salomón; Masnú, Simón; Montero, Pedro, and Rey, Carolina A. "Concentration Phenomena for Conformal Metrics with Constant Q-Curvature". arXiv preprint arXiv:2402.14675 (2024).

Alarcón, Salomón; Petean, Jimmy, and Rey, Carolina A. "Multiplicity results for constant Q-curvature conformal metrics". Calc. Var. 63, 146 (2024).

Rey, Carolina A., and Saintier, Nicolas. "Non-local equations and optimal Sobolev inequalities on compact manifolds". J Geom Anal 34, 17 (2024).

Rey, Carolina A., and Ruiz, Juan M. "Multipeak solutions for the Yamabe equation." The Journal of Geometric Analysis 31.2 (2021): 1180-1222.

Rey, Carolina A. "Elliptic equations with critical exponent on a torus invariant region of S3". Communications in Contemporary Mathematics 21.02 (2019): 1750100.

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