Researcher:
Coşkunüzer, Barış

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Barış

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Coşkunüzer

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Coşkunüzer, Barış

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2008 - 200932010 - 201712

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Researcher Of Publications: search.filters.isAuthorOfPublication.f02d184a-305e-4ad5-b6f3-7eeec1d5168a

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Now showing 1 - 10 of 15
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    Number of least area planes in gromov hyperbolic 3-spaces
    (American Mathematical Society (AMS), 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences; N/A
    We show that for a generic simple closed curve Gamma in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exists a unique least area plane Sigma in X such that partial derivative(infinity)Sigma = Gamma. This result has interesting topological applications for constructions of canonical 2-dimensional objects in Gromov hyperbolic 3-manifolds.
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    Properly embedded least area planes in gromov hyperbolic 3-spaces
    (American Mathematical Society (AMS), 2008) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let X be a Gromov hyperbolic 3-space with cocompact metric, and S 2∞ (X) the sphere at infinity of X. We show that for any simple closed curve ⌈ in S2∞ (X), there exists a properly embedded least area plane in X spanning r. This gives a positive answer to Gabai's conjecture from 1997. Soma has already proven this conjecture in 2004. Our technique here is simpler and more general, and it can be applied to many similar settings. © 2007 American Mathematical Society.
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    Generic uniqueness of area minimizing disks for extreme curves
    (Johns Hopkins Univ Press, 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences; N/A
    We show that for a generic nullhomotopic simple closed curve Gamma in the boundary of a compact, orientable. mean convex 3-manifold M with H-2(M, Z) = 0. there is a unique area minimizing disk D embedded in M with partial derivative D = Gamma. We also show that the same is true for nullhomologous curves in the absolutely area minimizing surface case.
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    Least area planes in hyperbolic 3-space are properly embedded
    (Indiana Univ Math Journal, 2009) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that if Sigma is an embedded least area (area minimizing) plane in H(3) whose asymptotic boundary is a simple closed curve with at least one smooth point, then Sigma is properly embedded in H(3).
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    H-surfaces with arbitrary topology in hyperbolic 3-space
    (Springer, 2017) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences; N/A
    We show that any open orientable surface can be properly embedded in H-3 as a constant mean curvature H-surface for H epsilon [0, 1). We obtain this result by proving a version of the bridge principle at infinity for H-surfaces. We also show that any open orientable surface can be nonproperly embedded in H-3 as a minimal surface.
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    PublicationOpen Access
    Examples of area-minimizing surfaces in 3-manifolds
    (Oxford University Press (OUP), 2012) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    In this paper, we give some examples of area-minimizing surfaces to clarify some wellknown features of these surfaces in more general settings. The first example is about Meeks–Yau’s result on the embeddedness of the solution to the Plateau problem. We construct an example of a simple closed curve in R3 which lies in the boundary of a mean convex domain in R3, but the area-minimizing disk in R3 bounding this curve is not embedded. Our second example shows that White’s boundary decomposition theorem does not extend when the ambient space has nontrivial homology. Our last examples show that there are properly embedded absolutely area-minimizing surfaces in a mean convex 3-manifold M such that, while their boundaries are disjoint, they intersect each other nontrivially, unlike the area-minimizing disks case.
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    Foliations of hyperbolic space by constant mean curvature hypersurfaces
    (Oxford University Press (OUP), 2009) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that the constant mean curvature hypersurfaces in Hn+1 spanning the boundary of a star-shaped C1,1 domain in Sn∞ (Hn+1) give a foliation of Hn+1. We also show that if is a closed codimension-1 C2,α submanifold in Sn∞ (Hn+1) bounding a unique constant mean curvature hypersurface H in Hn+1 with ∂∞ H = for any H ∈ (−1, 1), then the constant mean curvature hypersurfaces { H} foliate Hn+1.
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    PublicationOpen Access
    Number of Least area planes in gromov hyperbolic 3-spaces
    (American Mathematical Society (AMS), 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that for a generic simple closed curve Γ in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exists a unique least area plane Σ in X such that ∂∞Σ = Γ. This result has interesting topological applications for constructions of canonical 2-dimensional objects in Gromov hyperbolic 3-manifolds.
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    PublicationOpen Access
    Asymptotic H-Plateau problem in H-3
    (Mathematical Sciences Publishers (MSP), 2016) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that for any Jordan curve Gamma in S-infinity(2) (H-3) with at least one smooth point, there exists an embedded H-plane P-H in H-3 with partial derivative P-infinity(H) = Gamma for any H is an element of [0, 1).
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    Embedded plateau problem
    (American Mathematical Society (AMS), 2012) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that if Gamma is a simple closed curve bounding an embedded disk in a closed 3-manifold M, then there exists a disk Sigma in M with boundary Gamma such that Sigma minimizes the area among the embedded disks with boundary Gamma. Moreover, Sigma is smooth, minimal and embedded everywhere except where the boundary Gamma meets the interior of Sigma. The same result is also valid for homogeneously regular manifolds with sufficiently convex boundary.