S. Rosenberg

collaborators

5 papers

math.DG2026

Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain

Steven Rosenberg, Jie Xu

We introduce an iterative scheme to solve the Yamabe equation $- a I^_{g} u + S u = I^» u^{p - 1}$ on small domains $(I^c ◯, g) \subset R^{n}$ equipped with a Riemannian metric $g$ …

math.DG2026

The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds

Satoshi Egi, Yoshiaki Maeda, Steven Rosenberg

Let $M_{p}$ be a circle bundle with first Chern class $p [I ¨ ]$ over a closed $4 n$ -dimensional integral symplectic manifold $(M, I ¨ )$ . Equivalently, $M_{p}$ is a clos…

math.DG2026

The Conformal Laplacian and Positive Scalar Curvature Metrics on Manifolds with Boundary

Steven Rosenberg, Daniel Ruberman, Jie Xu

We give examples of spin $4$ -manifolds with boundary $(M, \partial M)$ such that the boundary $\partial M$ has a positive scalar curvature metric which cannot be extended to a posit…

cs.LG2025

Generalized Tangent Kernel: A Unified Geometric Foundation for Natural Gradient and Standard Gradient

Qinxun Bai, Steven Rosenberg, Wei Xu

Natural gradients have been widely studied from both theoretical and empirical perspectives, and it is commonly believed that natural gradients have advantages over standard (Eucli…

math.DG2025

The Geometry of Loop Spaces II: Characteristic Classes

Yoshiaki Maeda, Steven Rosenberg, FabiÃ¡n Torres-Ardila

Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2 k - 1} (L M)$ associated to the residue Chern character on the loop space $L M$ of a Riemannian manifold…