#geometric analysis
9 papers match
On two differing geometric descriptions of the passage from microscopy to macroscopy in Markov diffusion theory
Dalton A R Sakthivadivel
The paper builds a geometric framework that connects two different ways of passing from microscopic particle dynamics to macroscopic diffusion equations, by studying smooth probabi…
Mean curvature and sharp Willmore inequalities in metric spaces
Nicola Gigli, Ivan Yuri Violo
The paper defines a notion of mean curvature for level sets of Sobolev functions in non‑smooth metric spaces with Ricci curvature bounded below, introduces a Willmore functional, a…
Special Lagrangians with multiple isolated singularities
Bryan Dimler, Filippo Gaia
The paper extends a perturbation technique to construct special Lagrangian submanifolds in \(\mathbb{C}^m\) that have multiple prescribed isolated conical singularities, using a br…
A quantitative Schur comparison theorem for curves in CAT(k) spaces
Mohammad Ghomi, John Ioannis Stavroulakis
The paper provides a quantitative version of Schur's comparison theorem for curves with finite total curvature in CAT(k) spaces, extending classic results from Euclidean and Rieman…
GeoDetect: Geometric Adversarial Detection for VLPs
Afsaneh Hasanebrahimi, Hanxun Huang, Christopher Leckie +2
The paper introduces GeoDetect, a method that uses geometric properties of vision‑language model embeddings to detect adversarial examples by measuring how far they deviate from th…
Linearized heat semigroups on Finsler measure spaces and some applications
Qiaoling Xia
The paper investigates linearized heat semigroups on Finsler measure spaces, proving their conservativeness under lower bounds on weighted Ricci curvature and using this framework…