arXiv research

In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with nonpositive curvature. We show this result by constructing a non-properly embedded minimal plane in hyperbolic 3-space. Hence, this gives a counterexample to Calabi-Yau conj…

New surfaces in 3D space with constant curvature.

For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of $\mathrm{Diff}(\mathbb{S}^1)$ obtained are semi conjugate to subgroups of finite covers of $\mathrm{PSL}(2,\mathbb{R})$ by…

Abstract: Proves generic torus diffeomorphisms act parabolically and non-properly on fine curve graph and have generalized rotation sets.

Schoen-Webster theorem asserts a pseudoconvex CR manifold whose automorphism group acts non properly is either the standard sphere or the Heisenberg space. The purpose of this paper is to survey successive works around this result and then provide a short geometric proof in the compact case.

The study examines closed manifolds with ray nil-affine structures and their completeness.

Study closed manifolds with rank one ray structures, proving completeness or covering properties.

Embedding calculus proves convergence for surfaces.

Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.

The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.

New embedded periodic surfaces constructed in n-dimensional space.

Discrete maximal surfaces identified from s-embeddings.

This paper answers a question about discrete embeddings to maximal surfaces.

Maximizes symmetry of surfaces embedded in 3D space.

given two minimal surfaces embedded in $\S3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S3$ of genus $g$ that converges in $C^{2,α}$ to a compact embedded minimal surface provided some conditions are satisfied. These conditions also imply that, if any of th…

Geodesic surfaces embed into hyperbolic 3-manifolds for all finite group actions.

A surface in the 4-sphere is trivially embedded, if it bounds a 3-dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the Rokhlin quadratic form of this embedded surface.

Proves open Riemann surfaces can be embedded into 4D space.

In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; the…

Non-positively curved surfaces can be embedded in flat spacetime.

Proves surface embedding theorem for 4-manifolds with good fundamental group.

Essential embeddings of metric graphs on hyperbolic surfaces are constructed and studied.

For leveled spatial graphs, we find a surface embedding that allows cellular embedding.

Study proves only embedded free boundary surface in a ball is critical catenoid.

Classifies surfaces in Euclidean space with specific curvature relations.

For a non-orientable closed surface standardly embedded in the 4-sphere, a diffeomorphism over this surface is extendable if and only if this diffeomorphism preserves the Guillou-Marin quadratic form of this embedded surface.

Embedded surfaces in a ball have any genus and connected boundary.

The paper proves an adjunction inequality for Real embedded surfaces in 4-manifolds.

Constructs a family of genus three minimal surfaces with parallel ends.

Defines new gradings on Khovanov homology for surface embeddings.

Algorithm calculates genus of embedded graphs on surfaces.

Study extends surface embedding theorems to non-orientable cases.

The article discusses how to create a special type of triangle mesh for surfaces in 3D space.

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine …

Survey article on multibranched surfaces in 3-manifolds.

Embeddings preserve stable commutator length for surfaces.

Article provides conditions for embedding braid groups into mapping class groups.

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic embeddings in $\mathbb{R}^{3}$ of compact Riemann surfaces with finitely many punctures…

Sharp bounds on distortion of surfaces in 3D space.

Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvature of a surface embedded in a Riemannian manifold in terms of Poisson brackets of the embedding coordinates. We generalize these expressions to the pseudo-Riemannian setting and derive explicit formulas for the case of surfaces embedded in $\R^m…

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This dete…

Paper uses harmonic surfaces to model surfaces of any complexity.

Improved bound on first eigenvalue of minimal surfaces in $S^3$.

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space $\mathbb{H}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in $\mathbb{H}^3$ as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that t…

We prove the existence of embedded closed constant curvature curves on convex surfaces.

The paper explores shortest path embeddings on surfaces.