{"product_id":"9783832532062","title":"Constant Mean Curvature Surfaces in Homogeneous Manifolds","description":"\u003cp\u003eIn this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC Hsurfaces in igma( kappa) times mathbb{Rwith H in[0,1\/2]and kappa+4H^2 leq0, has genus 0, 2kends and k-fold dihedral symmetry, k geq2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1\/2surface in mathbb{H^2 times mathbb{Rwith kends, genus 1and k-fold dihedral symmetry, k geq3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1\/2all surfaces are Alexandrov-embedded.\u003c\/p\u003e","brand":"Logos Verlag","offers":[{"title":"Default Title","offer_id":47058393006320,"sku":"9783832532062","price":53.0,"currency_code":"USD","in_stock":false}],"url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783832532062","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}