The minimal surfa
ces in Finsler geometry with respe
ct to the Busemann–Hausdorff measure and the Holmes–
Thompson measure are
called BH-minimal and HT-minimal surfa
ces, respe
ctively. Let
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si1.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=17ca7f49269a057a79ca2d7783267e61" title="Click to view the MathML source">(p1,p2,p3,p4)class="mathContainer hidden">class="mathCode"> be the
coordinates of
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si2.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=32193ebbaa219b8934020f6e4586ee82" title="Click to view the MathML source">R4class="mathContainer hidden">class="mathCode"> and
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si292.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=00824cc64ac47f4cd030e03c7f285d99">
class="imgLazyJSB inlineImage" height="19" width="50" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si292.gif">cript>
cal-align:bottom" width="50" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si292.gif">cript>class="mathContainer hidden">class="mathCode"> be a Randers sphere of flag
curvature
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si4.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=01fee71a3b5566299393423c5cddf5fc" title="Click to view the MathML source">K=1class="mathContainer hidden">class="mathCode"> with the navigation data
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si5.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=d773311683ebbb041fdb7c1e47533996">
class="imgLazyJSB inlineImage" height="19" width="46" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si5.gif">cript>
cal-align:bottom" width="46" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si5.gif">cript>class="mathContainer hidden">class="mathCode">, where
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si293.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=0c0d0b996b44ab2c01d9523e31ba7929">
class="imgLazyJSB inlineImage" height="15" width="12" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si293.gif">cript>
cal-align:bottom" width="12" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si293.gif">cript>class="mathContainer hidden">class="mathCode"> is the standard sphere metri
c and
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si115.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=b65de1706b8d732754e06a8ae81490bb">
class="imgLazyJSB inlineImage" height="19" width="141" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si115.gif">cript>
cal-align:bottom" width="141" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si115.gif">cript>class="mathContainer hidden">class="mathCode">,
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si295.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=8ab37e9d5e497af3eb11e1a742a0d464" title="Click to view the MathML source">0<ε<1class="mathContainer hidden">class="mathCode">, is a Killing ve
ctor field. In this paper, we study the rotationally invariant minimal surfa
ce in
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si292.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=00824cc64ac47f4cd030e03c7f285d99">
class="imgLazyJSB inlineImage" height="19" width="50" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si292.gif">cript>
cal-align:bottom" width="50" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si292.gif">cript>class="mathContainer hidden">class="mathCode"> generated by rotating the
curve
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si9.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=cef3b639ebbd4b914b5c91ee1c2e1e53" title="Click to view the MathML source">(x(s),y(s),z(s),0)class="mathContainer hidden">class="mathCode"> in the upper half sphere of
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si10.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=9f1bfa289b9fdf9b56d7dbb209b81e1e" title="Click to view the MathML source">S2class="mathContainer hidden">class="mathCode"> around the
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si11.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=f9b9b28d70683b5132dd2738d2441dfa" title="Click to view the MathML source">p1p2class="mathContainer hidden">class="mathCode">-plane,
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si12.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=7af0d8f9caa756d009ae56c1d355d420" title="Click to view the MathML source">s∈Rclass="mathContainer hidden">class="mathCode">. We first show that su
ch a rotational BH-minimal surfa
ce in
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si292.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=00824cc64ac47f4cd030e03c7f285d99">
class="imgLazyJSB inlineImage" height="19" width="50" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si292.gif">cript>
cal-align:bottom" width="50" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si292.gif">cript>class="mathContainer hidden">class="mathCode"> is either a great 2-sphere or the
catenoid in
class="mathmlsrc">ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300506&_mathId=si13.gif&_user=111111111&_pii=S0022247X16300506&_rdoc=1&_issn=0022247X&md5=0b5523cace8e278bf2324b2f08f20508">
class="imgLazyJSB inlineImage" height="19" width="47" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16300506-si13.gif">cript>
cal-align:bottom" width="47" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16300506-si13.gif">cript>class="mathContainer hidden">class="mathCode">. Then we give a
classifi
cation of the rotational HT-minimal surfa
ces, where we use the
angle data to analyze the solutions of the system of ODE that
chara
cterizes the HT-minimality and prove that, su
ch a rotational HT-minimal surfa
ce must be a great 2-sphere, an HT-minimal torus, or a rotational surfa
ce of unduloid type. As a spe
cial
case, we obtain a distinguished embedded
compa
ct HT-minimal torus depending on
ε. The
completeness of these surfa
ces is also studied.