Surfaces in classical geometries
GR Jensen, E Musso, L Nicolodi - A Treatment by, 2016 - Springer
Research in differential geometry requires a broad core of knowledge. For over half a
century, this core has begun with the study of curves and surfaces in Euclidean space and …
century, this core has begun with the study of curves and surfaces in Euclidean space and …
Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure
We prove that every open Riemann surface $ M $ is the complex structure of a complete
surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space …
surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space …
The Cauchy problem for the Liouville equation and Bryant surfaces
JA Gálvez, P Mira - Advances in Mathematics, 2005 - Elsevier
We give a construction that connects the Cauchy problem for the 2-dimensional elliptic
Liouville equation with a certain initial value problem for mean curvature one surfaces in …
Liouville equation with a certain initial value problem for mean curvature one surfaces in …
Weierstrass-type representations
M Pember - Geometriae Dedicata, 2020 - Springer
Weierstrass-type representations | Geometriae Dedicata Skip to main content SpringerLink Log
in Menu Find a journal Publish with us Search Cart 1.Home 2.Geometriae Dedicata 3.Article …
in Menu Find a journal Publish with us Search Cart 1.Home 2.Geometriae Dedicata 3.Article …
Bryant surfaces with smooth ends
C Bohle, GP Peters - arxiv preprint math/0411480, 2004 - arxiv.org
A smooth end of a Bryant surface is a conformally immersed punctured disc of mean
curvature 1 in hyperbolic space that extends smoothly through the ideal boundary. The …
curvature 1 in hyperbolic space that extends smoothly through the ideal boundary. The …
Attaching handles to constant-mean-curvature-1 surfaces in hyperbolic 3-space
F Pacard, FAA Pimentel - Journal of the Institute of Mathematics of …, 2004 - cambridge.org
Using a connected sum construction, we prove the existence of complete non-compact
embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many …
embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many …
CMC-1 trinoids in hyperbolic 3-space and metrics of constant curvature one with conical singularities on the 2-sphere
S Fujimori, Y Kawakami, M Kokubu, W Rossman… - 2011 - projecteuclid.org
CMC-1 trinoids (ie constant mean curvature one immersed surfaces of genus zero with three
regular embedded ends) in hyperbolic 3-space H^3 are irreducible generically, and the …
regular embedded ends) in hyperbolic 3-space H^3 are irreducible generically, and the …
Björling formula for mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space
SD Yang - Bulletin of the Korean Mathematical Society, 2017 - koreascience.kr
We solve the $ Bj {\ddot {o}} rling $ problem for constant mean curvature one surfaces in
hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular …
hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular …
Loop Weierstrass Representation
T Raujouan, N Schmitt, J Ziefle - arxiv preprint arxiv:2411.04626, 2024 - arxiv.org
We introduce the Loop Weierstrass Representation for minimal surfaces in Euclidean space
and constant mean curvature 1 surfaces in hyperbolic space by applying integral system …
and constant mean curvature 1 surfaces in hyperbolic space by applying integral system …
Spacelike constant mean curvature 1 trinoids in de Sitter three-space
S Lee, SD Yang - 2006 - projecteuclid.org
SPACELIKE CONSTANT MEAN CURVATURE 1 TRINOIDS IN DE SITTER THREE-SPACE
Page 1 Lee, S. and Yang, S.-D. Osaka J. Math. 43 (2006), 641–663 SPACELIKE …
Page 1 Lee, S. and Yang, S.-D. Osaka J. Math. 43 (2006), 641–663 SPACELIKE …