BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Loops and Bubbles (4/4)
DTSTART;VALUE=DATE-TIME:20210421T150000Z
DTEND;VALUE=DATE-TIME:20210421T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-133@indico.eimi.ru
DESCRIPTION:Speakers: Roberta Musina ()\nAn important class of problems in
  Riemannian geometry can be stated as follows: given a smooth and orientab
 le Riemanninan manifold M\, find an hypersphere U in M having prescribed m
 ean curvature K at each point. We will be mainly focused on the case when 
 the target M is the Euclidean plane and the unknown U is a planar loop. Be
 sides its geometrical interpretation\, this (apparently) simple problem na
 turally arises in the study of the planar motion of an electrified particl
 e that experiences a Lorentz force produced by a magnetostatic field. It c
 an be regarded as a model for a more general question raised by V.I. Arnol
 d in [Uspekhi Mat. Nauk 1986]. We will first discuss some Alexandrov-type 
 uniqueness results in case the prescribed curvature is a positive constant
  or\, more generally\, a positive and radially non increasing function. To
  obtain existence results we will choose a parametric point of view\, whic
 h will lead us to study certain variational\, noncompact systems of second
  order ODE's for functions on the circle. This will give us the opportunit
 y to briefly introduce some variational (mountain pass lemma) and nonvaria
 tional (Lyapunov-Schmidt dimension reduction)basic techniques. In the last
  part of the course will overview some recent results and open problems in
  case the target space M is the hyperbolic plane\, or the Euclidean/hyperb
 olic 3-dimensional space.\n\nProgram:\n\n    The curvature of planar curve
 s. Planar loops and physical interpretation: a related ODE system and Arno
 l'd problem. Planar loops of positive curvature. Homework: the curvature o
 f circles and ellipses\, radially symmetric prescribed curvatures.\n    Th
 e four vertex theorem (Osserman's proof).\n    Uniqueness results: Alexand
 rov (1956)\, Aeppli (1960) and more (2011).\n    The (pseudo)-length funct
 ional and the weighted\, signed area functional.\n    The variational appr
 oach. A quick introduction to variational methods.\n    Palais-Smale condi
 tion\, the Mountain Pass Lemma\, saddle points.\n    A non-variational app
 roach: the Lyapunov-Schmidt dimension reduction.\n    Loops of prescribed 
 curvature in the hyperbolic plane. Bubbles in the Euclidean and in hyperbo
 lic spaces: recent results and open problems.\n\nhttps://indico.eimi.ru/ev
 ent/278/contributions/133/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loops and Bubbles (3/4)
DTSTART;VALUE=DATE-TIME:20210420T150000Z
DTEND;VALUE=DATE-TIME:20210420T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-132@indico.eimi.ru
DESCRIPTION:Speakers: Roberta Musina ()\nAn important class of problems in
  Riemannian geometry can be stated as follows: given a smooth and orientab
 le Riemanninan manifold M\, find an hypersphere U in M having prescribed m
 ean curvature K at each point. We will be mainly focused on the case when 
 the target M is the Euclidean plane and the unknown U is a planar loop. Be
 sides its geometrical interpretation\, this (apparently) simple problem na
 turally arises in the study of the planar motion of an electrified particl
 e that experiences a Lorentz force produced by a magnetostatic field. It c
 an be regarded as a model for a more general question raised by V.I. Arnol
 d in [Uspekhi Mat. Nauk 1986]. We will first discuss some Alexandrov-type 
 uniqueness results in case the prescribed curvature is a positive constant
  or\, more generally\, a positive and radially non increasing function. To
  obtain existence results we will choose a parametric point of view\, whic
 h will lead us to study certain variational\, noncompact systems of second
  order ODE's for functions on the circle. This will give us the opportunit
 y to briefly introduce some variational (mountain pass lemma) and nonvaria
 tional (Lyapunov-Schmidt dimension reduction)basic techniques. In the last
  part of the course will overview some recent results and open problems in
  case the target space M is the hyperbolic plane\, or the Euclidean/hyperb
 olic 3-dimensional space.\n\nProgram:\n\n    The curvature of planar curve
 s. Planar loops and physical interpretation: a related ODE system and Arno
 l'd problem. Planar loops of positive curvature. Homework: the curvature o
 f circles and ellipses\, radially symmetric prescribed curvatures.\n    Th
 e four vertex theorem (Osserman's proof).\n    Uniqueness results: Alexand
 rov (1956)\, Aeppli (1960) and more (2011).\n    The (pseudo)-length funct
 ional and the weighted\, signed area functional.\n    The variational appr
 oach. A quick introduction to variational methods.\n    Palais-Smale condi
 tion\, the Mountain Pass Lemma\, saddle points.\n    A non-variational app
 roach: the Lyapunov-Schmidt dimension reduction.\n    Loops of prescribed 
 curvature in the hyperbolic plane. Bubbles in the Euclidean and in hyperbo
 lic spaces: recent results and open problems.\n\nhttps://indico.eimi.ru/ev
 ent/278/contributions/132/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loops and Bubbles (2/4)
DTSTART;VALUE=DATE-TIME:20210414T150000Z
DTEND;VALUE=DATE-TIME:20210414T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-131@indico.eimi.ru
DESCRIPTION:Speakers: Roberta Musina ()\nAn important class of problems in
  Riemannian geometry can be stated as follows: given a smooth and orientab
 le Riemanninan manifold M\, find an hypersphere U in M having prescribed m
 ean curvature K at each point. We will be mainly focused on the case when 
 the target M is the Euclidean plane and the unknown U is a planar loop. Be
 sides its geometrical interpretation\, this (apparently) simple problem na
 turally arises in the study of the planar motion of an electrified particl
 e that experiences a Lorentz force produced by a magnetostatic field. It c
 an be regarded as a model for a more general question raised by V.I. Arnol
 d in [Uspekhi Mat. Nauk 1986]. We will first discuss some Alexandrov-type 
 uniqueness results in case the prescribed curvature is a positive constant
  or\, more generally\, a positive and radially non increasing function. To
  obtain existence results we will choose a parametric point of view\, whic
 h will lead us to study certain variational\, noncompact systems of second
  order ODE's for functions on the circle. This will give us the opportunit
 y to briefly introduce some variational (mountain pass lemma) and nonvaria
 tional (Lyapunov-Schmidt dimension reduction)basic techniques. In the last
  part of the course will overview some recent results and open problems in
  case the target space M is the hyperbolic plane\, or the Euclidean/hyperb
 olic 3-dimensional space.\n\nProgram:\n\n    The curvature of planar curve
 s. Planar loops and physical interpretation: a related ODE system and Arno
 l'd problem. Planar loops of positive curvature. Homework: the curvature o
 f circles and ellipses\, radially symmetric prescribed curvatures.\n    Th
 e four vertex theorem (Osserman's proof).\n    Uniqueness results: Alexand
 rov (1956)\, Aeppli (1960) and more (2011).\n    The (pseudo)-length funct
 ional and the weighted\, signed area functional.\n    The variational appr
 oach. A quick introduction to variational methods.\n    Palais-Smale condi
 tion\, the Mountain Pass Lemma\, saddle points.\n    A non-variational app
 roach: the Lyapunov-Schmidt dimension reduction.\n    Loops of prescribed 
 curvature in the hyperbolic plane. Bubbles in the Euclidean and in hyperbo
 lic spaces: recent results and open problems.\n\nhttps://indico.eimi.ru/ev
 ent/278/contributions/131/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loops and Bubbles (1/4)
DTSTART;VALUE=DATE-TIME:20210413T150000Z
DTEND;VALUE=DATE-TIME:20210413T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-130@indico.eimi.ru
DESCRIPTION:Speakers: Roberta Musina ()\nAn important class of problems in
  Riemannian geometry can be stated as follows: given a smooth and orientab
 le Riemanninan manifold M\, find an hypersphere U in M having prescribed m
 ean curvature K at each point. We will be mainly focused on the case when 
 the target M is the Euclidean plane and the unknown U is a planar loop. Be
 sides its geometrical interpretation\, this (apparently) simple problem na
 turally arises in the study of the planar motion of an electrified particl
 e that experiences a Lorentz force produced by a magnetostatic field. It c
 an be regarded as a model for a more general question raised by V.I. Arnol
 d in [Uspekhi Mat. Nauk 1986]. We will first discuss some Alexandrov-type 
 uniqueness results in case the prescribed curvature is a positive constant
  or\, more generally\, a positive and radially non increasing function. To
  obtain existence results we will choose a parametric point of view\, whic
 h will lead us to study certain variational\, noncompact systems of second
  order ODE's for functions on the circle. This will give us the opportunit
 y to briefly introduce some variational (mountain pass lemma) and nonvaria
 tional (Lyapunov-Schmidt dimension reduction)basic techniques. In the last
  part of the course will overview some recent results and open problems in
  case the target space M is the hyperbolic plane\, or the Euclidean/hyperb
 olic 3-dimensional space.\n\nProgram:\n\n    The curvature of planar curve
 s. Planar loops and physical interpretation: a related ODE system and Arno
 l'd problem. Planar loops of positive curvature. Homework: the curvature o
 f circles and ellipses\, radially symmetric prescribed curvatures.\n    Th
 e four vertex theorem (Osserman's proof).\n    Uniqueness results: Alexand
 rov (1956)\, Aeppli (1960) and more (2011).\n    The (pseudo)-length funct
 ional and the weighted\, signed area functional.\n    The variational appr
 oach. A quick introduction to variational methods.\n    Palais-Smale condi
 tion\, the Mountain Pass Lemma\, saddle points.\n    A non-variational app
 roach: the Lyapunov-Schmidt dimension reduction.\n    Loops of prescribed 
 curvature in the hyperbolic plane. Bubbles in the Euclidean and in hyperbo
 lic spaces: recent results and open problems.\n\nhttps://indico.eimi.ru/ev
 ent/278/contributions/130/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometric flows of networks (4/4)
DTSTART;VALUE=DATE-TIME:20210401T150000Z
DTEND;VALUE=DATE-TIME:20210401T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-129@indico.eimi.ru
DESCRIPTION:Speakers: Alessandra Pluda (Università di Pisa)\, Matteo Nova
 ga (Università di Pisa)\nhttps://indico.eimi.ru/event/278/contributions/1
 29/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometric flows of networks (3/4)
DTSTART;VALUE=DATE-TIME:20210330T150000Z
DTEND;VALUE=DATE-TIME:20210330T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-128@indico.eimi.ru
DESCRIPTION:Speakers: Alessandra Pluda (Università di Pisa)\, Matteo Nova
 ga (Università di Pisa)\nhttps://indico.eimi.ru/event/278/contributions/1
 28/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometric flows of networks (2/4)
DTSTART;VALUE=DATE-TIME:20210325T150000Z
DTEND;VALUE=DATE-TIME:20210325T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-127@indico.eimi.ru
DESCRIPTION:Speakers: Alessandra Pluda (Università di Pisa)\, Matteo Nova
 ga (Università di Pisa)\nhttps://indico.eimi.ru/event/278/contributions/1
 27/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometric flows of networks (1/4)
DTSTART;VALUE=DATE-TIME:20210323T150000Z
DTEND;VALUE=DATE-TIME:20210323T163000Z
DTSTAMP;VALUE=DATE-TIME:20260815T225420Z
UID:indico-contribution-278-126@indico.eimi.ru
DESCRIPTION:Speakers: Alessandra Pluda (Università di Pisa)\, Matteo Nova
 ga (Università di Pisa)\nhttps://indico.eimi.ru/event/278/contributions/1
 26/
LOCATION:Zoom 443 726 1792
URL:https://indico.eimi.ru/event/278/contributions/126/
END:VEVENT
END:VCALENDAR