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math.DG2025
On monotonicity of heat kernels: a new example and counterexamples
Almut Burchard, Ángel D. Martínez
We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity pro…
math.DG2024
Isometric embeddings
Ángel D. Martínez
In this paper we use the convex integration technique enhanced by an extra iteration originally due to Källén and revisited by Kröner to provide a local -principle for isometric…