arXiv subjects

Shunichiro Orikasa

Publications and source records attributed to Shunichiro Orikasa.

3 recordsLinked to original sources

arXiv2026

Linking at Infinity and Scalar Curvature Decay on Non-Compact Manifolds

We study complete non-compact manifolds of positive scalar curvature, with a focus on how curvature decay is constrained by topology at infinity. Our first main result shows that topological linking at infinity forces polynomial decay of scalar curvature on manifolds of weakly bounded geometry. This result provides a conceptual generalization of recently discovered examples of metrics with quadratic scalar curvature decay. Building on this decay mechanism, we develop an obstruction theory localized at the ends of non-compact manifolds. Using $μ$--bubble exhaustions together with the analysis of stable minimal hypersurfaces and index theory, we obtain qualitative obstructions to uniformly positive scalar curvature on individual ends.

math.DG↗

arXiv2025

Systolic Inequality and Scalar Curvature

We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with positive scalar curvature under a suitable stretch-scale condition. The proof combines techniques from geometric measure theory, reminiscent of Gromov's systolic inequality, with curvature estimates derived from the Gromov-Lawson relative index theorem. This approach provides a new framework for studying the relationship between positive scalar curvature metrics and systolic geometry in higher-dimensional manifolds.

math.DG↗

arXiv2025

Analysis of Contraction Mappings to The Complement of Closed Curves

We study some analytic properties of distance decreasing self-maps onto the complement of a smooth curve $Σ$ in $S^n$. For $n>4$ and $n\equiv 0 \mod 4$, let $Σ$ be an embedded circle in $S^n$ and let $g$ be a complete Riemannian metric on $X=S^n\backslash Σ$ and $f:(X,g)\to (X,g_{std})$ be a 1-contracting diffeomorphism. We verify the sharp estimate $\inf_{x\in X}Sc(g)_x C(n)\cdot \max_i\{|θ_i|\}$ where $W(Σ)$ is any tubular neighborhood of $Σ$ and $\{e^{2πiθ_i}\}_i$ are the holonomy parameters along $ι^*S^+$ where $S^+$ is the positive spinor bundle over $S^n$. This answers a question in \cite{gromov2018metric}.

math.DG↗