4 parts of the ligament help the jowls, jawline or marionette line?

Far more important than the technique is the skill and experience of your plastic surgeon. Choose your surgeon rather than the technique and let them explain why one technique may be better than another.  See the below link on some suggestions on finding the most qualified Plastic Surgeon for you.  Always insist on a board certified plastic surgeon.

I admire your effort to learn about anatomy underlying facial changes with aging. There are many components of this complex process and retaining ligaments are just a part of it. Visiting an interesting site sponsored by ASPS, understand.com,  may help you to understand principals of facial and neck lifting/shaping. Good luck.

The facial ligaments you are describing are what we call osteocutaneous ligaments. This means they are bands of connective tissue that anchor the skin to the underlying bone. When we are young these ligaments help keep the soft tissues of the face suspended. As we age the soft tissue descends but the ligaments usually stay taut. This becomes important in facelifting procedures because the soft tissues will not re-suspend well unless the facial retaining ligaments are released. This allows the descended tissue to move in the desired direction and be re-suspended using sutures. I divide all of the retaining ligaments (including the cervical ligament) in my facelifting procedures because I feel it produces the best and most durable result. Surgeons will have differing opinions on this topic so it is important to discuss it during your consultations. Best of luck!

Hello,
   Thank you for your question, we don’t often discuss anatomy here! specifically for the Jowl region there are 4 muscles of facial expression that are coalescing in this region. Zygomaticus major and minor from above and risorius as well as depressor Anguli oris from below. When we perform facelift surgery we actually work on the investing fascia of all the muscles and not the individual muscles themselves. This is where terms like “SMAS lift” come from. 
Hope that helps!
Dr G

Hi, I have performed many facelifts for over 30 years and have performed many minimally, invasive SMAS facelifts.  It's a bit complicated which is why we train for so many years to become facial plastic surgeons or general plastic surgeons that typically are the ones that perform facelifts.  Non smiling photos of your face from the front and side would help in the evaluation.  The bottom line is that the face has several layers of tissues that may or may not be adequately supported by the underlying cheek, chin and jaw bones.  In addition there may be excess fat or environmental factors that decrease the elasticity and tone in the skin.  All of these factors contribute to how fast and how much the face ages and sags.  As the face sags, the tissues rotate towards the midline creating nasolabial folds, jowls and excess skin below the chitin the neck.  Once this occurs, the most appropriate treatment is a proper SMAS facelift with facial shaping as described below.
  If you have "jowls” these are sagging facial tissues and the main indication for some form of a SMAS facelift.  The underlying SMAS layer, of the face, must be dissected, lifted, trimmed and re-sutured (not merely folded or suspended with threads or sutures that will not last).  The excess skin is then removed and the facelift incisions closed.
 My most popular SMAS facelift is the minimally invasive, short incision SMAS facelift that has all the benefits of more invasive facelifts (traditional, mid-face, deep plane, cheek lift and subperiosteal facelifts) but with these added benefits:
very small incisions and no incisions extend or are placed within the hair.
minimal tissue dissection = less bruising and swelling = rapid recovery ( several days instead of weeks or months with the more invasive type facelifts mentioned)
can be performed in 90 minutes or less, with or without general anesthesia
no incisions within the hair = no hair loss
excess fat can be removed from the face and neck
excess skin removed from the face and neck
cheeks, chin and jaw line can be augmented with dermal fillers (I prefer Restylane Lyft) or facial implants
most patients fly back home to parts all over the world in as little as 3 days post-op
 I combine facial shaping with every facelift procedure.  When jowls are present, these should be done in concert and not alone or separately in order to create a naturally, more attractive face. Following my beauty principles, women look the most feminine, youthful and attractive with heart shaped faces.  Heart shaped faces have cheeks that are full and round in the front.  Cheek augmentation with a dermal filler or using cheek implants for a permanent enhancement will create full, round cheeks that will feminize the entire face.
 A weak chin creates an imbalance making the nose appear larger, the mid face top heavy and the lower face look short that de-emphasizes the lips and allows early formation of a double chin.  Chin augmentation using a chin implant will add projection to the chin creating harmony and balance to the lower face.  I have found placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick and highly effective.
Hope this helps.

Not sure who is feeding you this information, but it is not true. There is NO ligaments which hold up the jowls. The jowls are a combination of skin and fat with underlying muscles- Masseter and Buccinator. When you age, the skin stretches by losing collagen and the fat descends by gravity. The treatment is removal of the fat and tightening the skin. There is no ligaments involved. Otherwise, it would be a much easier issue to deal with.