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Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics
Mohammad Javad Habibi Vosta Kolaei
https://arxiv.org/abs/2507.12068 ht…

Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics
We study the extrinsic geometry of isometric immersions into Riemannian manifolds of co-dimension one via a fourth-order geometric evolution of the shape operator. Motivated by bi-harmonic map theory and generalized Chen's conjecture, we introduce a moduli flow, a tensorial gradient flow that decreases a natural energy measuring curvature variation.

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Chunlin Wu, Zhenhua Wei, Huiming Yin
https://arxiv.org/abs/2506.16498

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Eshelby's problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-fields. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transien…