AT sectional Hawaii Honolulu UW Madison Dymarz Tullice Bowling - - PDF document

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AT sectional Hawaii Honolulu UW Madison Dymarz Tullice Bowling - - PDF document

Aug 01, 2023 481 likes •614 views

bilipschitz Quasi symmetric of of boundaries maps carved negatively homogeneous spaces AT sectional Hawaii Honolulu UW Madison Dymarz Tullice Bowling Green Xie Xiang dong Mapsbetweenmetricspacest X d LY d Qua si symmetric

slide-1
SLIDE 1

Quasi symmetric

bilipschitz

maps

  • f

boundaries

  • f

negatively

carved

homogeneous

spaces

AT

sectional

Honolulu

Hawaii Tullice

Dymarz

UW Madison

Xiangdong

Xie

Bowling Green

slide-2
SLIDE 2

Mapsbetweenmetricspacest

X d

LY

d

Quasi

symmetric

defilade 4957

Bi

lipschitzadkykdlflxlflylkbdlx.ly

similarity

dffixt

fly

adCxy

slide-3
SLIDE 3

Questions

For

which metric spaces

are

quasi symmetric

maps

bi Lipschitz

Under which

conditions

is

a

group

  • f

Lipschitz

quasi

symmetric

maps

a conjugate

  • f

a

group

  • f

similarities

slide-4
SLIDE 4

Themetricspacese

c

nilpotent

Lie gp

admitting family

N da

  • f

expanding

17

automorphisms

Parnaiba'd't

metric

IN

N

left

invariant

metric

such that

dacf.cm Etna

etdfn.in

A

IT

Hi

derivation

  • n

Seeta Indi on

with

Eigenvalues

with positiverepaatt

slide-5
SLIDE 5

y

N R2

Lx y

A

IE

dactyl

max

In

H ly yal

E T

N

Heisenberg

group

Cx y

2

3

A

iz

  • r

23 t

t

max

10 1,1091 1021k

max 10 1,19521021s

slide-6
SLIDE 6

Connections

to

Geometric TGroup

Theory

H

NAAR

is

negatively

curved

as

long

as

eigenvalues

  • f

A

have

positive

real

part

N AT

A

dis

Ha

RER

HP

e'd

N

Heisenberg

A

iz

Ha

NxR

a

ICHI

In

general

Hp

is

negatively

curved

homogeneous

space

slide-7
SLIDE 7

Boundaries

vertical

geodesi

2h13

R U

as

a Ha

N

da

VE

3

Nok

N

slide-8
SLIDE 8

Dictionary

DHA

Ha

quasi symmetric

quasi isometries

maps

bilipsmohaiptgJghueigshitires.EE

iie3

similarities

1

isometries

slide-9
SLIDE 9

Conjecture All

g

s

maps

  • f

LN da

are

bilip

unless

Ha

isometric to

symmetric space

Xie

Conjectured

Under

certain

conditions

uniformity

co compact

action

  • n

distinct

amenability

pairs

A

group

  • f

bi Lipschitz

maps

  • f

LN da

is the

conjugate of

a

group

  • f

similarities

  • f

Xie

Dymarz

N da

slide-10
SLIDE 10

Notes

case

  • f

Tukia

quasi conformal

maps

  • f

S

R

U DJ

D

htt

Chow

case

  • f

quasi conformal

maps

  • f

JEHM

Pansy

boundaries

  • f

remaining

symmetric

spaces

no

conjugation

needed

Xie

case

  • f

quasi conformal

maps

  • f

LNdA

Carnot groups

slide-11
SLIDE 11

Sometheoremsy

tie

Dymare

R

da

A diagonalizable

G

amenable uniform

group

  • f

biLipschitz

maps

then

it

is

a

conjugate

  • f

similarity

group

  • f

Ri

da

Heis

da

A 23

same

conclusion

In

progress

N da

A

diagonalizable