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Differential Geometry Papers @GeometryPapers

New Differential Geometry papers from arxiv.org: complex, contact, Riemannian. Thank you to arXiv for use of its open access interoperability.

Joined March 2010
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The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori, part II Oscar Perdomo arxiv.org/abs/2606.16980 [πš–πšŠπšπš‘.𝙳𝙢]

The stability index and Yau's conjecture for Carlotto-Schulz...

For any closed minimal hypersurface $M$ in the $N 1$-dimensional Euclidean sphere $S^{N 1}$, $-N$ is an eigenvalue of the stability operator. In this paper we show that the multiplicity of this...

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Complex Quaternions and Superminimal Surfaces in Four-Space Amedeo Altavilla, Elena Giorgio arxiv.org/abs/2606.16919 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.π™²πš…]

Complex Quaternions and Superminimal Surfaces in Four-Space

We develop a quaternionic approach to conformal superminimal surfaces in Euclidean four-space. The starting point is the classical Weierstrass representation: every conformal minimal immersion...

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Deformation theory of complex structures via Hamilton-Nash-Moser theory Vicente CortΓ©s, Paula Naomi Pilatus arxiv.org/abs/2606.16834 [πš–πšŠπšπš‘.𝙳𝙢]

Deformation theory of complex structures via Hamilton-Nash-Moser theory

We revisit the classical proof by Kuranishi on the existence of a locally complete family of complex deformations on a compact complex manifold using Hamilton's Nash-Moser implicit function...

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A diffeological perspective on non-Abelian Hodge theory Mahmud Azam, Steven Rayan arxiv.org/abs/2606.16772 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙢 πš–πšŠπšπš‘.π™²πšƒ πš–πšŠπšπš‘.π™²πš… πš–πšŠπšπš‘.πšπšƒ]

A diffeological perspective on non-Abelian Hodge theory

We construct diffeological moduli stacks $\mathscr{M}_{Dol}(X)$ and $\mathscr{M}_{dR}(X)$ parametrizing smooth families of Higgs bundles and those of flat bundles, respectively, on a compact...

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Comparison theorems in centro-affine differential geometry Yasuaki Fujitani arxiv.org/abs/2606.16654 [πš–πšŠπšπš‘.𝙳𝙢]

Comparison theorems in centro-affine differential geometry

For weighted manifolds with Bakry-Γ‰mery Ricci curvature bounded from below, comparison geometric results have been established. The Bakry-Γ‰mery Ricci curvature depends on the effective...

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Curvature at infinity of scalar-flat ALE four-manifolds Jiangcheng You arxiv.org/abs/2606.16176 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙿]

Curvature at infinity of scalar-flat ALE four-manifolds

We study refined asymptotics of scalar-flat ALE four-manifolds in the Tian--Viaclovsky setting, namely for self-dual or anti-self-dual metrics and for metrics with harmonic curvature. Starting...

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Admissibility, Topology, and the Οƒβ‚–-Loewner–Nirenberg problem Hao Fang, Matthew J. Gursky arxiv.org/abs/2606.16033 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙿]

Admissibility, Topology, and the $Οƒ_k$-Loewner--Nirenberg problem

The $Οƒ_k$-Loewner--Nirenberg problem is a fully nonlinear generalization of the classical Loewner--Nirenberg problem of constructing complete conformal metrics with constant negative scalar...

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KΓ€hler-Ricci Flow: from divisors to cusps Eleonora Di Nezza, Vincent Guedj, Chinh H. Lu arxiv.org/abs/2606.15816 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙿 πš–πšŠπšπš‘.π™²πš…]

KΓ€hler-Ricci Flow: from divisors to cusps

We study the geometric regularization of positive closed currents by the KΓ€hler-Ricci flow on compact KΓ€hler manifolds. In a previous work of ours, it was shown that the KΓ€hler-Ricci flow...

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Entire area-minimizing surfaces in Rⁿ of density two are quadratic or planar Nick Edelen, Luis Atzin Franco Reyna, Paul Minter arxiv.org/abs/2606.15795 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙿]

Entire area-minimizing surfaces in $\mathbf{R}^n$ of density two...

We classify any entire area-minimizing surface $M^2\subset\mathbf{R}^n$ with density $2$ at infinity as either planar or algebraic, namely the zero set of a quadratic holomorphic polynomial (up to...

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On the non-existence of symphonic maps Ahmed Mohammed Cherif, Kaddour Zegga arxiv.org/abs/2606.15790 [πš–πšŠπšπš‘.𝙳𝙢]

On the non-existence of symphonic maps

In this paper, we study the existence of symphonic maps on compact or complet non-compact Riemannian manifold into Riemannian manifolds admitting a conformal vector field or a non-trivial Ricci...

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Scalar curvature rigidity for products of convex hypersurfaces Samuel Lockman, Rudolf Zeidler arxiv.org/abs/2606.15710 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.π™Ίπšƒ]

Scalar curvature rigidity for products of convex hypersurfaces

Let $N = N_{1} \times \dotsm \times N_{k}$, where each $N_{i} \subset \mathbb{R}^{n_i 1}$ is a closed strictly convex hypersurface. Let $M$ be a Riemannian spin manifold of dimension $n =...

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Killing Vectors and Bochner-Type Theorems in Pseudo-Riemannian Hom-Lie Algebras Raymond Hounnonkpe, Ibrahima Bakayoko, Emmanuel Gnandi, Joel Tossa arxiv.org/abs/2606.15704 [πš–πšŠπšπš‘.𝙳𝙢]

Killing Vectors and Bochner-Type Theorems in Pseudo-Riemannian...

In this paper, we study pseudo-Riemannian Hom-Lie algebras. We establish Hom-versions of the classical Bochner theorem in both the Riemannian and Lorentzian settings. Finally, we prove that the...

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On Locally Dually and Projectively Flat Almost Rational Finsler Metrics Ghanashyam Kumar Prajapati, Ranadip Gangopadhyay, Bankteshwar Tiwari arxiv.org/abs/2606.15699 [πš–πšŠπšπš‘.𝙳𝙢]

On Locally Dually and Projectively Flat Almost Rational Finsler Metrics

In this paper, we investigate Almost Rational Finsler (AR-Finsler) metrics, a class of Finsler metrics whose fundamental tensor admits a decomposition $g_{ij}(x,y)=Ξ·(x,y)a_{ij}(x,y),$ where...

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Quadratic one-forms on logarithmic Higgs moduli Sumit Roy arxiv.org/abs/2606.15560 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.𝙰𝙢]

Quadratic one-forms on logarithmic Higgs moduli

Let $C$ be a compact Riemann surface of genus at least two, and let $G$ be a connected complex reductive group. We study logarithmic \(G\)-Higgs bundles on a pointed curve $(C,D)$ whose residues...

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Gromov's Euclidean Endpoint C⁰ Rigidity for the Positive Mass Theorem Jiangcheng You, Heng Zhang arxiv.org/abs/2606.15372 [πš–πšŠπšπš‘.𝙳𝙢]

Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive...

We prove Gromov's Euclidean endpoint $C^0$ rigidity conjecture. Let $g$ be a smooth complete metric on $\R^3$ with non-negative scalar curvature. If $$ |g-g_{\Euc}|=o(r^{-1}),\qquad...

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Existence of twisted Hermitian-Einstein metrics on unstable vector bundles Mingwei Wang, Xiaokui Yang, Shing-Tung Yau arxiv.org/abs/2606.15102 [πš–πšŠπšπš‘.𝙳𝙢]

Existence of twisted Hermitian-Einstein metrics on unstable vector bundles

In this paper, we demonstrate that twisted Hermitian-Einstein metrics on holomorphic vector bundles exist without obstruction. More precisely, for an arbitrary holomorphic vector bundle $E$ over a...

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The Cone Projection f(z)=dfracz1 |z|/R Geometric structure and the Self-Directrix Theorem George M. Georgiou arxiv.org/abs/2606.14915 [πš–πšŠπšπš‘.𝙳𝙢]

The Cone Projection $f(z)=\dfrac{z}{1 |z|/R}$ Geometric structure...

The \emph{cone projection} $f_R(z)=z/(1 |z|/R)$ arises from an elementary spatial construction: join a point of the complex plane to the center of a cone's base, mark where that segment meets the...

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Holomorphic families of knots Rodion DΓ©ev, Vasily Rogov arxiv.org/abs/2606.14429 [πš–πšŠπšπš‘.𝙳𝙢 πš–πšŠπšπš‘.π™²πš…]

Holomorphic families of knots

Let $(M, [g])$ be a $3$-dimensional conformal manifold. The space of knots $\mathrm{Kn}(M)$ in $M$ is an infinite-dimensional manifold that is known to carry an almost complex structure. This...

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Gaussian-Weighted Curvature Gaps for Self-Shrinkers Fagui Li, Yuhang Zhao arxiv.org/abs/2606.14360 [πš–πšŠπšπš‘.𝙳𝙢]

Gaussian-Weighted Curvature Gaps for Self-Shrinkers

In this paper, we prove lower bounds for the Gaussian-weighted \(L^2\)-curvature integral of embedded self-shrinkers. The proof combines normal coordinate functions with weighted PoincarΓ©...

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Ricci solitons from the perspectives of energy function Shubham Yadav, Hemangi Madhusudan Shah arxiv.org/abs/2606.14336 [πš–πšŠπšπš‘.𝙳𝙢]

Ricci solitons from the perspectives of energy function

In this article, we explore to what extent the geometry of gradient Ricci solitons can be carried over to the geometry of non-gradient Ricci solitons. We use energy function $E$ of the soliton as...

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