Neron models of Green-Griffiths-Kerr and log Neron models

For a variation of Hodge structure over a punctured disk, Green, Griffiths and Kerr introduced a N'eron model which is a Hausdorff space that includes values of admissible normal functions. On the other hand, Kato, Nakayama and Usui introduced a N'eron model as a logarithmic manifold using log mixed Hodge theory. This work constructs a homeomorphism between these two models.