{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T19:27:50Z","timestamp":1770492470537,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/00212\/2019"],"award-info":[{"award-number":["UID\/MAT\/00212\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Monatsh Math"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s00605-021-01516-w","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T12:31:57Z","timestamp":1611923517000},"page":"625-656","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Harmonic maps and shift-invariant subspaces"],"prefix":"10.1007","volume":"194","author":[{"given":"Alexandru","family":"Aleman","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2380","authenticated-orcid":false,"given":"Rui","family":"Pacheco","sequence":"additional","affiliation":[]},{"given":"John C.","family":"Wood","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,29]]},"reference":[{"key":"1516_CR1","unstructured":"Aleman, A., Pacheco, R., Wood, J.C.: Symmetric shift-invariant subspaces and harmonic maps. Math. Z. (to appear). Preprint available at arXiv:1908.01557"},{"key":"1516_CR2","volume-title":"The Cauchy Transform, Potential Theory and Conformal Mapping","author":"SR Bell","year":"2016","unstructured":"Bell, S.R.: The Cauchy Transform, Potential Theory and Conformal Mapping, 2nd edn. Chapman & Hall, Boca Raton (2016)","edition":"2"},{"key":"1516_CR3","first-page":"36","volume":"398","author":"A Bahy-El-Dien","year":"1989","unstructured":"Bahy-El-Dien, A., Wood, J.C.: The explicit construction of all harmonic two-spheres in $$G_2({ R}^n)$$. J. Reine Angew. Math. 398, 36\u201366 (1989)","journal-title":"J. Reine Angew. Math."},{"key":"1516_CR4","first-page":"119","volume":"459","author":"J Bolton","year":"1995","unstructured":"Bolton, J., Pedit, F., Woodward, L.M.: Minimal surfaces and the affine Toda field model. J. Reine Angew. Math. 459, 119\u2013150 (1995)","journal-title":"J. Reine Angew. Math."},{"key":"1516_CR5","unstructured":"Bolton, J., Woodward, L.M.: The affine Toda equations and minimal surfaces. In: Harmonic Maps and Integrable Systems, pp. 59\u201382. Vieweg, Braunschweig (1994). http:\/\/www.maths.leeds.ac.uk\/pure\/staff\/wood\/FordyWood\/contents.html"},{"key":"1516_CR6","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1215\/S0012-7094-95-08015-6","volume":"80","author":"FE Burstall","year":"1995","unstructured":"Burstall, F.E., Pedit, F.: Dressing orbits of harmonic maps. Duke Math. J. 80, 353\u2013382 (1995)","journal-title":"Duke Math. J."},{"key":"1516_CR7","doi-asserted-by":"publisher","first-page":"255","DOI":"10.4310\/jdg\/1214440115","volume":"23","author":"FE Burstall","year":"1986","unstructured":"Burstall, F.E., Wood, J.C.: The construction of harmonic maps into complex Grassmannians. J. Differ. Geom. 23, 255\u2013298 (1986)","journal-title":"J. Differ. Geom."},{"key":"1516_CR8","doi-asserted-by":"crossref","unstructured":"Cheeger, J., Ebin, D.G.: Comparison Theorems in Riemannian Geometry. Revised reprint of the 1975 original, AMS Chelsea Publishing, Providence. RI (2008)","DOI":"10.1090\/chel\/365"},{"issue":"2","key":"1516_CR9","doi-asserted-by":"publisher","first-page":"301","DOI":"10.2307\/1971312","volume":"125","author":"S-S Chern","year":"1987","unstructured":"Chern, S.-S., Wolfson, J.G.: Harmonic maps of the two-sphere into a complex Grassmann manifold II. Ann. Math. (2) 125(2), 301\u2013335 (1987)","journal-title":"Ann. Math. (2)"},{"issue":"4","key":"1516_CR10","doi-asserted-by":"publisher","first-page":"633","DOI":"10.4310\/CAG.1998.v6.n4.a1","volume":"6","author":"J Dorfmeister","year":"1998","unstructured":"Dorfmeister, J., Pedit, F., Wu, H.: Weierstrass type representation of harmonic maps into symmetric spaces. Commun. Anal. Geom. 6(4), 633\u2013668 (1998)","journal-title":"Commun. Anal. Geom."},{"key":"1516_CR11","doi-asserted-by":"crossref","unstructured":"Eells, J., Lemaire, L.: Selected Topics in Harmonic Maps, CBMS Regional Conference Series, vol. 50, Amer. Math. Soc. (1983)","DOI":"10.1090\/cbms\/050"},{"issue":"1","key":"1516_CR12","doi-asserted-by":"publisher","first-page":"109","DOI":"10.2307\/2373037","volume":"86","author":"J Eells","year":"1964","unstructured":"Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. Am. J. Math. 86(1), 109\u2013160 (1964)","journal-title":"Am. J. Math."},{"key":"1516_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1112\/jlms\/s2-28.1.161","volume":"28","author":"S Erdem","year":"1983","unstructured":"Erdem, S., Wood, J.C.: On the construction of harmonic maps into a Grassmannian. J. Lond. Math. Soc. (2) 28, 161\u2013174 (1983)","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"1516_CR14","doi-asserted-by":"crossref","unstructured":"Forster, O.: Lectures on Riemann Surfaces, Translated from the 1977 German Original by Bruce Gilligan. Reprint of the 1981 English Translation. Graduate Texts in Mathematics, vol. 81. Springer, New York (1991)","DOI":"10.1007\/978-1-4612-5961-9"},{"key":"1516_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139174848","volume-title":"Harmonic Maps, Loop Groups, and Integrable Systems, London Mathematical Society Student Texts","author":"MA Guest","year":"1997","unstructured":"Guest, M.A.: Harmonic Maps, Loop Groups, and Integrable Systems, London Mathematical Society Student Texts, vol. 38. Cambridge University Press, Cambridge (1997)"},{"key":"1516_CR16","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198565994.001.0001","volume-title":"From Quantum Cohomology to Integrable Systems, Oxford Graduate Texts in Mathematics","author":"MA Guest","year":"2008","unstructured":"Guest, M.A.: From Quantum Cohomology to Integrable Systems, Oxford Graduate Texts in Mathematics, vol. 15. Oxford University Press, Cambridge (2008)"},{"key":"1516_CR17","doi-asserted-by":"publisher","first-page":"750","DOI":"10.2307\/2373697","volume":"95","author":"RD Gulliver","year":"1973","unstructured":"Gulliver, R.D., Osserman, R., Royden, H.L.: A theory of branched immersions of surfaces. Am. J. Math. 95, 750\u2013812 (1973)","journal-title":"Am. J. Math."},{"key":"1516_CR18","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/BF01351803","volume":"135","author":"H Grauert","year":"1958","unstructured":"Grauert, H.: Analytische Faserungen \u00fcber holomorph-vollst\u00e4ndigen R\u00e4umen. Math. Ann 135, 263\u2013273 (1958)","journal-title":"Math. Ann"},{"key":"1516_CR19","volume-title":"Lectures on Invariant Subspaces","author":"H Helson","year":"1964","unstructured":"Helson, H.: Lectures on Invariant Subspaces. Academic Press, New York (1964)"},{"issue":"1","key":"1516_CR20","doi-asserted-by":"publisher","first-page":"113","DOI":"10.4310\/jdg\/1214457033","volume":"42","author":"GR Jensen","year":"1995","unstructured":"Jensen, G.R., Liao, R.: Families of flat minimal tori in $$CP^n$$. J. Differ. Geom. 42(1), 113\u2013132 (1995)","journal-title":"J. Differ. Geom."},{"key":"1516_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0541-8","volume-title":"Fundamentals of Differential Geometry, Graduate Texts in Mathematics","author":"S Lang","year":"1999","unstructured":"Lang, S.: Fundamentals of Differential Geometry, Graduate Texts in Mathematics, vol. 191. Springer, New York (1999)"},{"key":"1516_CR22","volume-title":"Functional Analysis, Pure and Applied Mathematics","author":"PD Lax","year":"2002","unstructured":"Lax, P.D.: Functional Analysis, Pure and Applied Mathematics. Wiley, New York (2002)"},{"key":"1516_CR23","doi-asserted-by":"crossref","unstructured":"Nikol\u2019skii, N.K.: Treatise on the shift operator. Spectral function theory, Grundlehren der Mathematischen Wissenschaften, vol. 273. Springer, Berlin (1986)","DOI":"10.1007\/978-3-642-70151-1"},{"key":"1516_CR24","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1112\/plms\/s3-61.3.546","volume":"61","author":"Y Ohnita","year":"1990","unstructured":"Ohnita, Y., Valli, G.: Pluriharmonic maps into compact Lie groups and factorization into unitons. Proc. Lond. Math. Soc. 61, 546\u2013570 (1990)","journal-title":"Proc. Lond. Math. Soc."},{"key":"1516_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21681-2","volume-title":"Hankel Operators and Their Applications","author":"V Peller","year":"2003","unstructured":"Peller, V.: Hankel Operators and Their Applications. Springer, New York (2003)"},{"key":"1516_CR26","volume-title":"Loop Groups. Oxford Mathematical Monographs","author":"A Pressley","year":"1986","unstructured":"Pressley, A., Segal, G.: Loop Groups. Oxford Mathematical Monographs. Oxford University Press, Oxford (1986)"},{"key":"1516_CR27","doi-asserted-by":"crossref","unstructured":"Segal, G.: Loop Groups and Harmonic Maps, Advances in Homotopy Theory (Cortona, 1988). London Mathematical Society Lecture Note Series, pp. 153\u2013164, vol. 139, Cambridge Univ. Press, Cambridge (1989)","DOI":"10.1017\/CBO9780511662614.015"},{"key":"1516_CR28","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s00220-011-1398-3","volume":"310","author":"M Svensson","year":"2012","unstructured":"Svensson, M., Wood, J.C.: Filtrations, factorizations and explicit formulae for harmonic maps. Commun. Math. Phys. 310, 99\u2013134 (2012)","journal-title":"Commun. Math. Phys."},{"key":"1516_CR29","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/s00229-014-0659-9","volume":"44","author":"M Svensson","year":"2014","unstructured":"Svensson, M., Wood, J.C.: New constructions of twistor lifts for harmonic maps. Manuscr. Math. 44, 457\u2013502 (2014)","journal-title":"Manuscr. Math."},{"key":"1516_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4310\/jdg\/1214443286","volume":"30","author":"K Uhlenbeck","year":"1989","unstructured":"Uhlenbeck, K.: Harmonic maps into Lie groups: classical solutions of the chiral model. J. Differ. Geom. 30, 1\u201350 (1989)","journal-title":"J. Differ. Geom."},{"key":"1516_CR31","unstructured":"Urakawa, H.: Calculus of Variations and Harmonic Maps, Translations of Mathematical Monographs, vol. 132. Amer. Math. Soc. (1993)"},{"key":"1516_CR32","doi-asserted-by":"crossref","unstructured":"Wood, J.C.: Explicit constructions of harmonic maps. In: Loubeau, E., Montaldo, S. (eds.) Harmonic Maps and Differential Geometry. Contemporary Mathematics, vol. 542, pp. 41\u201374. Amer. Math. Soc. (2011)","DOI":"10.1090\/conm\/542\/10698"},{"key":"1516_CR33","volume-title":"Low-Dimensional Sigma Models","author":"WJ Zakrzewski","year":"1989","unstructured":"Zakrzewski, W.J.: Low-Dimensional Sigma Models. Adam Hilger Ltd, Bristol (1989)"}],"container-title":["Monatshefte f\u00fcr Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00605-021-01516-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00605-021-01516-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00605-021-01516-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T05:42:09Z","timestamp":1724391729000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00605-021-01516-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,29]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["1516"],"URL":"https:\/\/doi.org\/10.1007\/s00605-021-01516-w","relation":{},"ISSN":["0026-9255","1436-5081"],"issn-type":[{"value":"0026-9255","type":"print"},{"value":"1436-5081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,29]]},"assertion":[{"value":"30 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 January 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}