S. Rosenberg

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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…

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…