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Prescribed Chern scalar curvatures on complete Hermitian manifolds
Weike Yu
https://arxiv.org/abs/2506.14592 https://arxiv.org/pdf/25…

Prescribed Chern scalar curvatures on complete Hermitian manifolds
In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete Hermitian manifolds. Firstly, we re-prove our recent result for prescribing sign-changing Chern scalar curvatures on compact Hermitian manifolds by using the classical maximum principle. Secondly, we study this problem on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results [J. Differential Geom., 21 (1985): 269-281] from Poincaré disks to higher dimensional Her…

This https://arxiv.org/abs/2403.07698 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Kazdan-Warner problem on compact Kähler surfaces
In this paper, we investigate a Kazdan-Warner problem on compact Kähler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact Kähler surfaces when the candidate curvature function is of negative average. Moreover, we give an alternative proof of Ding-Liu's theorem [Trans. Amer. Math. Soc. 347(1995) 1059-1066] on prescribing sign-changing Gaussian curvatures.

Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface
Francesco Vicentini, Jonas Heinzmann, Pietro Carrara, Laura De Lorenzis
https://arxiv.org/abs/2506.12188

Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these models lack flexibility in prescribing material-specific strength surfaces. Consequently, they struggle to accurately capture crack nucleation under multiaxial stress conditions. In this paper, inspired by Alessi et al. (2014), we propose a variational phase-f…