Fixed Points of Automorphisms of the Vector Bundle Moduli Space Over a Compact Riemann Surface

Fixed-Point Results of Generalized (ϕ,Ψ)-Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations

“…Then, by the hypothesis, we have gu p ⪯ g ü for all p ∈ N. Now, we will examine that ü is a coincidence point of h and g. By applying (23), we obtain…”

“…Brzdęk et al [21] proved a fixed point theorem and the Ulam stability in generalized dq-metric spaces. Antón-Sancho [22,23] presented fixed points of principal E six-bundles over a compact algebraic curve and of the automorphisms of the vector bundle moduli space over a compact Riemann surface.…”

Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold

“…The above condition is a generalization of the stability condition for vector bundles, which plays an important role in the study of moduli spaces of vector bundles and other geometric objects. Over the past few years, the exploration of moduli spaces of vector bundles and various geometric objects has attracted considerable interest and focus (see [27][28][29][30][31][32][33][34][35] and references therein).…”

“…When R exhibits analytic (σ, τ)-stability relative to the Hermitian metric K, we aim to demonstrate that, by selecting a subsequence, H ε approaches a (σ, τ)-Hermite-Yang-Mills metric H in the C ∞ loc -topology as ε tends to 0. Leveraging the local C 1 -estimates from (27) alongside standard elliptic theory, our focus narrows to deriving a uniform C 0estimate. Thanks to Lemma 4, our task simplifies to establishing a consistent bound on…”

Constant Angle Ruled Surfaces with a Pointwise 1-Type Gauss Map

“…The fact that the curvatures and normal directions are important components of the vector bundle structures shows us the crucial link between the Gauss map and the geometric properties of vector bundles. Recent research on vector bundles over surfaces and curves includes the vector bundle moduli spaces over Riemann surfaces [13], the moduli space of Higgs bundles [14,15], as well as vector bundles discussed in [16,17]. The Gauss map can also visualize vector bundles' transition functions, sections, and moduli spaces, providing insights into the geometric structures of principal bundles over compact algebraic curves that were recently studied in [18].…”