Willmore deformations between minimal surfaces in Hn+2 and Sn+2
In this paper we show that locally there exists a Willmore deformation between minimal surfaces in S n + 2 and minimal surfaces in H n + 2 , i.e., there exists a smooth family of Willmore surfaces { y t : U ~ → S n + 2 , t ∈ [ 0 , 2 π ) } such that ( y t ) | t = 0 is conformally equivalent to a mini...
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| Veröffentlicht in: | Mathematische Zeitschrift 2023, Vol.303 (1) |
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| creator | Wang, Changping Wang, Peng |
| description | In this paper we show that locally there exists a Willmore deformation between minimal surfaces in
S
n
+
2
and minimal surfaces in
H
n
+
2
, i.e., there exists a smooth family of Willmore surfaces
{
y
t
:
U
~
→
S
n
+
2
,
t
∈
[
0
,
2
π
)
}
such that
(
y
t
)
|
t
=
0
is conformally equivalent to a minimal surface in
S
n
+
2
and
(
y
t
)
|
t
=
π
/
2
is conformally equivalent to a minimal surface in
H
n
+
2
. Here
U
~
is a simply connected open subset of the surface
M
. For some cases the deformations are global. By the Willmore deformations of the Veronese two-sphere and its generalizations in
S
4
, for any positive number
W
0
∈
R
+
, we construct complete minimal surfaces in
H
4
with Willmore energy being equal to
W
0
. An example of complete minimal Möbius strip in
H
4
with Willmore energy
6
5
π
5
≈
10.733
π
is also presented. We also show that all isotropic minimal surfaces in
S
4
admit Jacobi fields different from Killing fields, i.e., they are not “isolated”. |
| doi_str_mv | 10.1007/s00209-022-03169-3 |
| format | Article |
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S
n
+
2
and minimal surfaces in
H
n
+
2
, i.e., there exists a smooth family of Willmore surfaces
{
y
t
:
U
~
→
S
n
+
2
,
t
∈
[
0
,
2
π
)
}
such that
(
y
t
)
|
t
=
0
is conformally equivalent to a minimal surface in
S
n
+
2
and
(
y
t
)
|
t
=
π
/
2
is conformally equivalent to a minimal surface in
H
n
+
2
. Here
U
~
is a simply connected open subset of the surface
M
. For some cases the deformations are global. By the Willmore deformations of the Veronese two-sphere and its generalizations in
S
4
, for any positive number
W
0
∈
R
+
, we construct complete minimal surfaces in
H
4
with Willmore energy being equal to
W
0
. An example of complete minimal Möbius strip in
H
4
with Willmore energy
6
5
π
5
≈
10.733
π
is also presented. We also show that all isotropic minimal surfaces in
S
4
admit Jacobi fields different from Killing fields, i.e., they are not “isolated”.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-022-03169-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Deformation ; Equivalence ; Mathematics ; Mathematics and Statistics ; Minimal surfaces</subject><ispartof>Mathematische Zeitschrift, 2023, Vol.303 (1)</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00209-022-03169-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00209-022-03169-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Wang, Changping</creatorcontrib><creatorcontrib>Wang, Peng</creatorcontrib><title>Willmore deformations between minimal surfaces in Hn+2 and Sn+2</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>In this paper we show that locally there exists a Willmore deformation between minimal surfaces in
S
n
+
2
and minimal surfaces in
H
n
+
2
, i.e., there exists a smooth family of Willmore surfaces
{
y
t
:
U
~
→
S
n
+
2
,
t
∈
[
0
,
2
π
)
}
such that
(
y
t
)
|
t
=
0
is conformally equivalent to a minimal surface in
S
n
+
2
and
(
y
t
)
|
t
=
π
/
2
is conformally equivalent to a minimal surface in
H
n
+
2
. Here
U
~
is a simply connected open subset of the surface
M
. For some cases the deformations are global. By the Willmore deformations of the Veronese two-sphere and its generalizations in
S
4
, for any positive number
W
0
∈
R
+
, we construct complete minimal surfaces in
H
4
with Willmore energy being equal to
W
0
. An example of complete minimal Möbius strip in
H
4
with Willmore energy
6
5
π
5
≈
10.733
π
is also presented. We also show that all isotropic minimal surfaces in
S
4
admit Jacobi fields different from Killing fields, i.e., they are not “isolated”.</description><subject>Deformation</subject><subject>Equivalence</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Minimal surfaces</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkMFKxDAURYMoOI7-gKuAS4kmL0nTrEQGxxEGXKi4DG3zIh3atCYd_H2rI7i6D-7hXTiEXAp-Izg3t5lz4JZxAMalKCyTR2QhlAQmSpDHZDH3munSqFNylvOO87k0akHu3tuu64eE1GMYUl9N7RAzrXH6Qoy0b2PbVx3N-xSqBjNtI93Ea6BV9PRlPs7JSai6jBd_uSRv64fX1YZtnx-fVvdbNgptJua9D6oypfVFUwZVNtxyWWMJEEBLgcEoFQz4QjdNjQJUEQwC1EY32kqwckmuDn_HNHzuMU9uN-xTnCcdGGWsMFaJmZIHKo-pjR-Y_inB3Y8pdzDlZlPu15ST8hsjgFo_</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Wang, Changping</creator><creator>Wang, Peng</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2023</creationdate><title>Willmore deformations between minimal surfaces in Hn+2 and Sn+2</title><author>Wang, Changping ; Wang, Peng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-dddf4a789d6c8f48c0903be822f2531ef744f72d65ccbe1246f7e22b75c593293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Deformation</topic><topic>Equivalence</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Minimal surfaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Changping</creatorcontrib><creatorcontrib>Wang, Peng</creatorcontrib><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Changping</au><au>Wang, Peng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Willmore deformations between minimal surfaces in Hn+2 and Sn+2</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2023</date><risdate>2023</risdate><volume>303</volume><issue>1</issue><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>In this paper we show that locally there exists a Willmore deformation between minimal surfaces in
S
n
+
2
and minimal surfaces in
H
n
+
2
, i.e., there exists a smooth family of Willmore surfaces
{
y
t
:
U
~
→
S
n
+
2
,
t
∈
[
0
,
2
π
)
}
such that
(
y
t
)
|
t
=
0
is conformally equivalent to a minimal surface in
S
n
+
2
and
(
y
t
)
|
t
=
π
/
2
is conformally equivalent to a minimal surface in
H
n
+
2
. Here
U
~
is a simply connected open subset of the surface
M
. For some cases the deformations are global. By the Willmore deformations of the Veronese two-sphere and its generalizations in
S
4
, for any positive number
W
0
∈
R
+
, we construct complete minimal surfaces in
H
4
with Willmore energy being equal to
W
0
. An example of complete minimal Möbius strip in
H
4
with Willmore energy
6
5
π
5
≈
10.733
π
is also presented. We also show that all isotropic minimal surfaces in
S
4
admit Jacobi fields different from Killing fields, i.e., they are not “isolated”.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-022-03169-3</doi></addata></record> |
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| issn | 0025-5874 1432-1823 |
| language | eng |
| recordid | cdi_proquest_journals_2747917941 |
| source | Springer Nature |
| subjects | Deformation Equivalence Mathematics Mathematics and Statistics Minimal surfaces |
| title | Willmore deformations between minimal surfaces in Hn+2 and Sn+2 |
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