3 papers
math.DG2026
The -equivariant Kazdan--Warner problem
Leonardo F. Cavenaghi, João Marcos do Ã, Llohann D. Sperança
We establish an equivariant analogue of the Kazdan--Warner trichotomy for admissible scalar curvature functions. Let be a closed connected manifold of dimension equip…
math.DG2026
The curvature of convex sum of metrics and applications
Leonardo F. Cavenaghi, Giovane Galindo, Llohann D. Sperança
In this note, we derive explicit formulae for the curvature of a convex sum of Riemannian metrics, \(g_t = (1-t)g_0 + t g_1\). We study whether such a deformation can increase the…
math.CO2025
Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0
Vladimir Blinovsky, Llohann D. Sperança, Alexander Pchelintsev
Assuming that Brouwers Conjecture the upper bound for the sum of t< n largest eigenvalues of Laplacian graph on n vertices true for n <n_0, we prove the Brouwers Conjecture BC for…