The Lipschitz continuity of the distance function to the cut locus. Zbl 0971.53031
Itoh, Jin-ichi; Tanaka, Minoru |
|
2001
|
The geometry of total curvature on complete open surfaces. Zbl 1086.53056
Shiohama, Katsuhiro; Shioya, Takashi; Tanaka, Minoru |
|
2003
|
Cut loci and distance spheres on Alexandrov surfaces. Zbl 0874.53032
Shiohama, Katsuhiro; Tanaka, Minoru |
|
1996
|
Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Zbl 1184.53036
Bonnard, Bernard; Caillau, Jean-Baptiste; Sinclair, Robert; Tanaka, Minoru |
|
2009
|
The dimension of a cut locus on a smooth Riemannian manifold. Zbl 0939.53029
Itoh, Jin-Ichi; Tanaka, Minoru |
|
1998
|
On the cut loci of a von Mangoldt’s surface of revolution. Zbl 0789.53023
Tanaka, Minoru |
|
1992
|
The cut locus of a two-sphere of revolution and Toponogov’s comparison theorem. Zbl 1158.53033
Sinclair, Robert; Tanaka, Minoru |
|
2007
|
On the existence of infinitely many isometry-invariant geodesics. Zbl 0499.53041
Tanaka, Minoru |
|
1982
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II. Zbl 1225.53034
Kondo, Kei; Tanaka, Minoru |
|
2010
|
On the number of invariant closed geodesics. Zbl 0375.58010
Grove, Karsten; Tanaka, Minoru |
|
1978
|
The cut locus and distance function from a closed subset of a Finsler manifold. Zbl 1358.53080
Sabau, Sorin V.; Tanaka, Minoru |
|
2016
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I. Zbl 1243.53072
Kondo, Kei; Tanaka, Minoru |
|
2011
|
The cut locus of a torus of revolution. Zbl 1080.53005
Gravesen, Jens; Markvorsen, Steen; Sinclair, Robert; Tanaka, Minoru |
|
2005
|
The length function of geodesic parallel circles. Zbl 0799.53052
Shiohama, Katsuhiro; Tanaka, Minoru |
|
1993
|
On a characterization of a surface of revolution with many poles. Zbl 0781.53034
Tanaka, Minoru |
|
1992
|
Loki: software for computing cut loci. Zbl 1052.53001
Sinclair, Robert; Tanaka, Minoru |
|
2002
|
Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below. Zbl 1020.53019
Shiohama, Katsuhiro; Tanaka, Minoru |
|
2002
|
Toponogov comparison theorem for open triangles. Zbl 1243.53066
Kondo, Kei; Tanaka, Minoru |
|
2011
|
A bound on the number of endpoints of the cut locus. Zbl 1111.53004
Sinclair, Robert; Tanaka, Minoru |
|
2006
|
A Sard theorem for the distance function. Zbl 1046.53016
Itoh, Jin-ichi; Tanaka, Minoru |
|
2001
|
An isoperimetric problem for infinitely connected complete open surfaces. Zbl 0697.53040
Shiohama, K.; Tanaka, M. |
|
1989
|
Mass of rays on complete open surfaces. Zbl 0731.53044
Shiohama, K.; Shioya, T.; Tanaka, M. |
|
1990
|
On the number of invariant closed geodesics. Zbl 0325.58010
Grove, Karsten; Tanaka, Minoru |
|
1976
|
Jacobi’s last geometric statement extends to a wider class of Liouville surfaces. Zbl 1124.53015
Sinclair, Robert; Tanaka, Minoru |
|
2006
|
The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces. Zbl 1266.53041
Tanaka, Minoru; Kondo, Kei |
|
2013
|
Approximations of Lipschitz maps via immersions and differentiable exotic sphere theorems. Zbl 1368.49053
Kondo, Kei; Tanaka, Minoru |
|
2017
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III. Zbl 1246.53055
Kondo, Kei; Tanaka, Minoru |
|
2012
|
On invariant closed geodesics under isometries. Zbl 0364.58014
Tanaka, Minoru |
|
1977
|
Characterization of a differentiable point of the distance function to the cut locus. Zbl 1037.53022
Tanaka, Minoru |
|
2003
|
Compact Riemannian manifolds which are isospectral to three dimensional lens spaces. II. Zbl 0436.53046
Tanaka, Minoru |
|
1979
|
Topology of complete Finsler manifolds with radial flag curvature bounded below. Zbl 1319.53082
Kondo, Kei; Ohta, Shin-ichi; Tanaka, Minoru |
|
2014
|
Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces. Zbl 1227.53053
Kondo, Kei; Tanaka, Minoru |
|
2011
|
On the compact minimal submanifold in Riemannian manifolds. Zbl 0978.53110
Lu, Jin; Tanaka, Minoru |
|
2000
|
An elementary proof of the existence of uncountably many nonclosed isometry-invariant geodesics. Zbl 0736.53045
Tanaka, Minoru |
|
1991
|
A new family of latitudinally corrugated two-spheres of revolution with simple cut locus structure. Zbl 1519.53009
Tanaka, Minoru; Akamatsu, Toyohiro; Sinclair, Robert; Yamaguchi, Masaru |
|
2023
|
The set of poles of a two-sheeted hyperboloid. Zbl 1052.53002
Sinclair, Robert; Tanaka, Minoru |
|
2002
|
The singular locus of an almost distance function. Zbl 1445.53035
Tanaka, Minoru |
|
2020
|
Invariant closed geodesics under isometries of prime power order. Zbl 0426.58007
Tanaka, Minoru |
|
1977
|
Closed geodesics on compact Riemannian manifolds with infinite fundamental groups. Zbl 0581.53034
Tanaka, Minoru |
|
1985
|
Relativistic effects in the search for new intra-atomic force with isotope shifts. Zbl 1477.81133
Tanaka, Minoru; Yamamoto, Yasuhiro |
|
2020
|
A new family of latitudinally corrugated two-spheres of revolution with simple cut locus structure. Zbl 1519.53009
Tanaka, Minoru; Akamatsu, Toyohiro; Sinclair, Robert; Yamaguchi, Masaru |
|
2023
|
The singular locus of an almost distance function. Zbl 1445.53035
Tanaka, Minoru |
|
2020
|
Relativistic effects in the search for new intra-atomic force with isotope shifts. Zbl 1477.81133
Tanaka, Minoru; Yamamoto, Yasuhiro |
|
2020
|
Approximations of Lipschitz maps via immersions and differentiable exotic sphere theorems. Zbl 1368.49053
Kondo, Kei; Tanaka, Minoru |
|
2017
|
The cut locus and distance function from a closed subset of a Finsler manifold. Zbl 1358.53080
Sabau, Sorin V.; Tanaka, Minoru |
|
2016
|
Topology of complete Finsler manifolds with radial flag curvature bounded below. Zbl 1319.53082
Kondo, Kei; Ohta, Shin-ichi; Tanaka, Minoru |
|
2014
|
The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces. Zbl 1266.53041
Tanaka, Minoru; Kondo, Kei |
|
2013
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III. Zbl 1246.53055
Kondo, Kei; Tanaka, Minoru |
|
2012
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I. Zbl 1243.53072
Kondo, Kei; Tanaka, Minoru |
|
2011
|
Toponogov comparison theorem for open triangles. Zbl 1243.53066
Kondo, Kei; Tanaka, Minoru |
|
2011
|
Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces. Zbl 1227.53053
Kondo, Kei; Tanaka, Minoru |
|
2011
|
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II. Zbl 1225.53034
Kondo, Kei; Tanaka, Minoru |
|
2010
|
Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Zbl 1184.53036
Bonnard, Bernard; Caillau, Jean-Baptiste; Sinclair, Robert; Tanaka, Minoru |
|
2009
|
The cut locus of a two-sphere of revolution and Toponogov’s comparison theorem. Zbl 1158.53033
Sinclair, Robert; Tanaka, Minoru |
|
2007
|
A bound on the number of endpoints of the cut locus. Zbl 1111.53004
Sinclair, Robert; Tanaka, Minoru |
|
2006
|
Jacobi’s last geometric statement extends to a wider class of Liouville surfaces. Zbl 1124.53015
Sinclair, Robert; Tanaka, Minoru |
|
2006
|
The cut locus of a torus of revolution. Zbl 1080.53005
Gravesen, Jens; Markvorsen, Steen; Sinclair, Robert; Tanaka, Minoru |
|
2005
|
The geometry of total curvature on complete open surfaces. Zbl 1086.53056
Shiohama, Katsuhiro; Shioya, Takashi; Tanaka, Minoru |
|
2003
|
Characterization of a differentiable point of the distance function to the cut locus. Zbl 1037.53022
Tanaka, Minoru |
|
2003
|
Loki: software for computing cut loci. Zbl 1052.53001
Sinclair, Robert; Tanaka, Minoru |
|
2002
|
Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below. Zbl 1020.53019
Shiohama, Katsuhiro; Tanaka, Minoru |
|
2002
|
The set of poles of a two-sheeted hyperboloid. Zbl 1052.53002
Sinclair, Robert; Tanaka, Minoru |
|
2002
|
The Lipschitz continuity of the distance function to the cut locus. Zbl 0971.53031
Itoh, Jin-ichi; Tanaka, Minoru |
|
2001
|
A Sard theorem for the distance function. Zbl 1046.53016
Itoh, Jin-ichi; Tanaka, Minoru |
|
2001
|
On the compact minimal submanifold in Riemannian manifolds. Zbl 0978.53110
Lu, Jin; Tanaka, Minoru |
|
2000
|
The dimension of a cut locus on a smooth Riemannian manifold. Zbl 0939.53029
Itoh, Jin-Ichi; Tanaka, Minoru |
|
1998
|
Cut loci and distance spheres on Alexandrov surfaces. Zbl 0874.53032
Shiohama, Katsuhiro; Tanaka, Minoru |
|
1996
|
The length function of geodesic parallel circles. Zbl 0799.53052
Shiohama, Katsuhiro; Tanaka, Minoru |
|
1993
|
On the cut loci of a von Mangoldt’s surface of revolution. Zbl 0789.53023
Tanaka, Minoru |
|
1992
|
On a characterization of a surface of revolution with many poles. Zbl 0781.53034
Tanaka, Minoru |
|
1992
|
An elementary proof of the existence of uncountably many nonclosed isometry-invariant geodesics. Zbl 0736.53045
Tanaka, Minoru |
|
1991
|
Mass of rays on complete open surfaces. Zbl 0731.53044
Shiohama, K.; Shioya, T.; Tanaka, M. |
|
1990
|
An isoperimetric problem for infinitely connected complete open surfaces. Zbl 0697.53040
Shiohama, K.; Tanaka, M. |
|
1989
|
Closed geodesics on compact Riemannian manifolds with infinite fundamental groups. Zbl 0581.53034
Tanaka, Minoru |
|
1985
|
On the existence of infinitely many isometry-invariant geodesics. Zbl 0499.53041
Tanaka, Minoru |
|
1982
|
Compact Riemannian manifolds which are isospectral to three dimensional lens spaces. II. Zbl 0436.53046
Tanaka, Minoru |
|
1979
|
On the number of invariant closed geodesics. Zbl 0375.58010
Grove, Karsten; Tanaka, Minoru |
|
1978
|
On invariant closed geodesics under isometries. Zbl 0364.58014
Tanaka, Minoru |
|
1977
|
Invariant closed geodesics under isometries of prime power order. Zbl 0426.58007
Tanaka, Minoru |
|
1977
|
On the number of invariant closed geodesics. Zbl 0325.58010
Grove, Karsten; Tanaka, Minoru |
|
1976
|
