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Latest papers

1. Post-Newtonian theory in de Sitter and anti-de Sitter spacetimes hep-th · 14 Oct · 2 hits

   …algebra, corresponding to the isometry algebra of the (A)dS background, is realised in phase space as a curvature-dependent deformation of the Poincare algebra at each PN order. Our results provide a systematic…

2. Proof of the Penrose Conjecture for Maximally Parameterized Initial Data Sets math.DG · 14 Oct · 1 hit

   …identities produce a Riemannian comparison metric \[ \bar g=g+\beta\otimes\beta \] with nonnegative scalar curvature $R_{\bar{g}} \geq 0$. Under a natural nondegeneracy condition (5.7) at the apparent horizon, the…

3. Cheng's Theorem in the Spectral Setting math.DG · 14 Oct · 2 hits

   …rigidity theorem for closed 3-dimensional Riemannian manifolds under a spectral lower bound for the Ricci curvature. We show that if $0<\gamma<2$, $K>0$ and $\lambda_1(-\gamma\Delta+\operatorname{Ric})\geq 2K$, then…

4. Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators math.DG · 14 Oct · 1 hit

   In this short note, using OpenAI's resolution of the Solomon--Yau conjecture, we extend our joint work with…

5. K-area bounds for smooth sphere bundles math.DG · 14 Oct · 1 hit

   …where $n\ge2$. We prove K-area$(E,g)\le4\pi n(n-1)/\sigma$ whenever every fibre has intrinsic scalar curvature at least $\sigma>0$, independently of the dimension of $B$. In particular, unit round fibres give…

6. One Size Does Not Fit All: Curvature-Aware Adaptive Perturbation for SAM cs.LG · 14 Oct · 3 hits

   …towards flat minima. However, SAM relies on a fixed perturbation radius $\rho$ that ignores local curvature, leading to inefficient behaviour: the perturbation may be too small to escape poor basins defined…

7. Dynamic morphing of non-Euclidean active shells enabled by flutter under a steady stimulus cond-mat.soft · 14 Oct · 1 hit

   …the non-Euclidean framework for thin structures to account for field-induced activity through a spontaneous curvature evolving in time with the system configuration. Examining elliptic plates and cylindrical shells as…

8. Odd mapping cone Chern character math.DG · 14 Oct · 1 hit

   …established the mapping cone Chern character on the even-degree side, using the powers of the mapping cone curvature associated with the given mapping cone connection. In this paper, we carry out the odd-degree…